5013:
independent at high strain-rates. A dislocation-based extension based on is used at low strain-rates. The SCGL model is used extensively by the shock physics community. The
Zerilli–Armstrong (ZA) model is a simple physically based model that has been used extensively. A more complex model that is based on ideas from dislocation dynamics is the Mechanical Threshold Stress (MTS) model. This model has been used to model the plastic deformation of copper, tantalum, alloys of steel, and aluminum alloys. However, the MTS model is limited to strain-rates less than around 10/s. The Preston–Tonks–Wallace (PTW) model is also physically based and has a form similar to the MTS model. However, the PTW model has components that can model plastic deformation in the overdriven shock regime (strain-rates greater that 10/s). Hence this model is valid for the largest range of strain-rates among the five flow stress models.
3850:
3497:
9619:
2911:
11176:
3845:{\displaystyle {\begin{aligned}&{\boldsymbol {\varepsilon }}={\boldsymbol {\varepsilon }}_{\mathrm {e} }={\mathsf {E}}^{-1}~{\boldsymbol {\sigma }}=~{\boldsymbol {\varepsilon }}&&\mathrm {for} ~||{\boldsymbol {\sigma }}||<\sigma _{y}\\&{\dot {\boldsymbol {\varepsilon }}}={\dot {\boldsymbol {\varepsilon }}}_{\mathrm {e} }+{\dot {\boldsymbol {\varepsilon }}}_{\mathrm {vp} }={\mathsf {E}}^{-1}~{\dot {\boldsymbol {\sigma }}}+f({\boldsymbol {\sigma }},\sigma _{y},{\boldsymbol {\varepsilon }}_{\mathrm {vp} })~{\boldsymbol {\sigma }}&&\mathrm {for} ~||{\boldsymbol {\sigma }}||\geq \sigma _{y}\end{aligned}}}
9029:
2592:
10502:
4212:
9614:{\displaystyle {\begin{aligned}\theta (\sigma _{e})&=\theta _{0}+\theta _{IV}F(\sigma _{e})\\\theta _{0}&=a_{0}+a_{1}\ln {\dot {\varepsilon _{\rm {p}}}}+a_{2}{\sqrt {\dot {\varepsilon _{\rm {p}}}}}-a_{3}T\\F(\sigma _{e})&={\cfrac {\tanh \left(\alpha {\cfrac {\sigma _{e}}{\sigma _{es}}}\right)}{\tanh(\alpha )}}\\\ln({\cfrac {\sigma _{es}}{\sigma _{0es}}})&=\left({\frac {kT}{g_{0es}b^{3}\mu (p,T)}}\right)\ln \left({\cfrac {\dot {\varepsilon _{\rm {p}}}}{\dot {\varepsilon _{\rm {p}}}}}\right)\end{aligned}}}
3896:
2906:{\displaystyle {\begin{aligned}&{\boldsymbol {\sigma }}={\mathsf {E}}~{\boldsymbol {\varepsilon }}&&\mathrm {for} ~\|{\boldsymbol {\sigma }}\|<\sigma _{y}\\&{\dot {\boldsymbol {\varepsilon }}}={\dot {\boldsymbol {\varepsilon }}}_{\mathrm {e} }+{\dot {\boldsymbol {\varepsilon }}}_{\mathrm {vp} }={\mathsf {E}}^{-1}~{\dot {\boldsymbol {\sigma }}}+{\cfrac {\boldsymbol {\sigma }}{\eta }}\left&&\mathrm {for} ~\|{\boldsymbol {\sigma }}\|\geq \sigma _{y}\end{aligned}}}
11171:{\displaystyle {\begin{aligned}\tau _{s}&=\max \left\{s_{0}-(s_{0}-s_{\infty }){\rm {{erf}\left,s_{0}\left({\cfrac {\dot {\varepsilon _{\rm {p}}}}{\gamma {\dot {\xi }}}}\right)^{s_{1}}}}\right\}\\\tau _{y}&=\max \left\{y_{0}-(y_{0}-y_{\infty }){\rm {{erf}\left,\min \left\{y_{1}\left({\cfrac {\dot {\varepsilon _{\rm {p}}}}{\gamma {\dot {\xi }}}}\right)^{y_{2}},s_{0}\left({\cfrac {\dot {\varepsilon _{\rm {p}}}}{\gamma {\dot {\xi }}}}\right)^{s_{1}}\right\}}}\right\}\end{aligned}}}
22:
3475:
4207:{\displaystyle {\dot {\varepsilon }}_{\mathrm {vp} }={\cfrac {\left\langle f({\boldsymbol {\sigma }},{\boldsymbol {q}})\right\rangle }{\tau }}{\cfrac {\partial f}{\partial {\boldsymbol {\sigma }}}}={\begin{cases}{\cfrac {f({\boldsymbol {\sigma }},{\boldsymbol {q}})}{\tau }}{\cfrac {\partial f}{\partial {\boldsymbol {\sigma }}}}&{\rm {if}}~f({\boldsymbol {\sigma }},{\boldsymbol {q}})>0\\0&{\rm {otherwise}}\\\end{cases}}}
677:
4799:
3859:
2538:
885:
1063:
1490:
1423:. In models where the elements are connected in series the strain is additive while the stress is equal in each element. In parallel connections, the stress is additive while the strain is equal in each element. Many of these one-dimensional models can be generalized to three dimensions for the small strain regime. In the subsequent discussion, time rates strain and stress are written as
485:
10210:
3467:
6095:
3322:
4595:
2551:
1681:
5604:
898:
7432:
1335:
1196:
9927:
8120:
3331:
5825:
3077:
5012:
The
Johnson–Cook (JC) model is purely empirical and is the most widely used of the five. However, this model exhibits an unrealistically small strain-rate dependence at high temperatures. The Steinberg–Cochran–Guinan–Lund (SCGL) model is semi-empirical. The model is purely empirical and strain-rate
1339:
Therefore, the relaxation curve can be used to determine rate of viscoplastic strain and hence the viscosity of the dashpot in a one-dimensional viscoplastic material model. The residual value that is reached when the stress has plateaued at the end of a relaxation test corresponds to the upper limit
892:
As shown in Figure 4, the relaxation test is defined as the stress response due to a constant strain for a period of time. In viscoplastic materials, relaxation tests demonstrate the stress relaxation in uniaxial loading at a constant strain. In fact, these tests characterize the viscosity and can be
2586:
For elastic-perfectly viscoplastic materials, the elastic strain is no longer considered negligible but the rate of plastic strain is only a function of the initial yield stress and there is no influence of hardening. The sliding element represents a constant yielding stress when the elastic limit
2320:
655:
is the viscoplastic strain. To obtain the stress–strain behavior shown in blue in the figure, the material is initially loaded at a strain rate of 0.1/s. The strain rate is then instantaneously raised to 100/s and held constant at that value for some time. At the end of that time period the strain
7871:
4501:
48:
which means that the material undergoes unrecoverable deformations when a load level is reached. Rate-dependent plasticity is important for transient plasticity calculations. The main difference between rate-independent plastic and viscoplastic material models is that the latter exhibit not only
687:
is the tendency of a solid material to slowly move or deform permanently under constant stresses. Creep tests measure the strain response due to a constant stress as shown in Figure 3. The classical creep curve represents the evolution of strain as a function of time in a material subjected to
3491:
is described by equations similar to those for an elastic-viscoplastic material with perfect plasticity. However, in this case the stress depends both on the plastic strain rate and on the plastic strain itself. For an elastoviscoplastic material the stress, after exceeding the yield stress,
2558:
Two types of elementary approaches can be used to build up an elastic-perfectly viscoplastic mode. In the first situation, the sliding friction element and the dashpot are arranged in parallel and then connected in series to the elastic spring as shown in Figure 7. This model is called the
2533:
These models can be applied in metals and alloys at temperatures higher than two thirds of their absolute melting point (in kelvins) and polymers/asphalt at elevated temperature. The responses for strain hardening, creep, and relaxation tests of such material are shown in Figure 6.
1571:
10342:
5405:
1939:
669:
11604:
586:
2529:
7260:
6761:
328:, with superposed effects of inter-crystalline gliding. The mechanism usually becomes dominant at temperatures greater than approximately one third of the absolute melting temperature. However, certain alloys exhibit viscoplasticity at room temperature (300 K). For
4794:{\displaystyle {\dot {\varepsilon }}_{\mathrm {vp} }={\begin{cases}{\mathsf {C}}^{-1}:{\cfrac {{\boldsymbol {\sigma }}-{\mathcal {P}}{\boldsymbol {\sigma }}}{\tau }}&{\rm {{if}~f({\boldsymbol {\sigma }},{\boldsymbol {q}})>0}}\\0&{\rm {otherwise}}\end{cases}}}
688:
uniaxial stress at a constant temperature. The creep test, for instance, is performed by applying a constant force/stress and analyzing the strain response of the system. In general, as shown in Figure 3b this curve usually shows three phases or periods of behavior:
1205:
2084:
1072:
5274:
873:
808:
5819:
The
Steinberg–Cochran–Guinan–Lund (SCGL) model is a semi-empirical model that was developed by Steinberg et al. for high strain-rate situations and extended to low strain-rates and bcc materials by Steinberg and Lund. The flow stress in this model is given by
1414:
One-dimensional constitutive models for viscoplasticity based on spring-dashpot-slider elements include the perfectly viscoplastic solid, the elastic perfectly viscoplastic solid, and the elastoviscoplastic hardening solid. The elements may be connected in
7954:
656:
rate is dropped instantaneously back to 0.1/s and the cycle is continued for increasing values of strain. There is clearly a lag between the strain-rate change and the stress response. This lag is modeled quite accurately by overstress models (such as the
3068:
7065:
1058:{\displaystyle {\cfrac {\mathrm {d} {\boldsymbol {\varepsilon }}}{\mathrm {d} t}}={\cfrac {\mathrm {d} {\boldsymbol {\varepsilon }}_{\mathrm {e} }}{\mathrm {d} t}}+{\cfrac {\mathrm {d} {\boldsymbol {\varepsilon }}_{\mathrm {vp} }}{\mathrm {d} t}}~.}
9020:
8690:
2210:
7728:
4399:
7549:
9921:
The
Preston–Tonks–Wallace (PTW) model attempts to provide a model for the flow stress for extreme strain-rates (up to 10/s) and temperatures up to melt. A linear Voce hardening law is used in the model. The PTW flow stress is given by
4987:
plasticity. In those situations the plastic strain rate is calculated in the same manner as in rate-independent plasticity. In other situations, the yield stress model provides a direct means of computing the plastic strain rate.
2164:
743:
1340:
of elasticity. For some materials such as rock salt such an upper limit of elasticity occurs at a very small value of stress and relaxation tests can be continued for more than a year without any observable plateau in the stress.
1497:
In a perfectly viscoplastic solid, also called the Norton-Hoff model of viscoplasticity, the stress (as for viscous fluids) is a function of the rate of permanent strain. The effect of elasticity is neglected in the model, i.e.,
10205:{\displaystyle {\text{(6)}}\qquad \sigma _{y}(\varepsilon _{\rm {p}},{\dot {\varepsilon _{\rm {p}}}},T)={\begin{cases}2\left\right]\mu (p,T)&{\text{thermal regime}}\\2\tau _{s}\mu (p,T)&{\text{shock regime}}\end{cases}}}
3462:{\displaystyle {\dot {\boldsymbol {\varepsilon }}}={\mathsf {E}}^{-1}~{\dot {\boldsymbol {\sigma }}}+f({\boldsymbol {\sigma }},\sigma _{y})~{\boldsymbol {\sigma }}\quad \mathrm {for} ~\|{\boldsymbol {\sigma }}\|\geq \sigma _{y}}
1404:
6090:{\displaystyle {\text{(2)}}\qquad \sigma _{y}(\varepsilon _{\rm {p}},{\dot {\varepsilon _{\rm {p}}}},T)=\left{\frac {\mu (p,T)}{\mu _{0}}};\quad \sigma _{a}f\leq \sigma _{\text{max}}~~{\text{and}}~~\sigma _{t}\leq \sigma _{p}}
3317:{\displaystyle {\dot {\boldsymbol {\varepsilon }}}={\mathsf {E}}^{-1}~{\dot {\boldsymbol {\sigma }}}+{\cfrac {\boldsymbol {\sigma }}{\lambda }}\left^{N-1}\left\quad \mathrm {for} ~\|{\boldsymbol {\sigma }}\|\geq \sigma _{y}}
488:
Figure 2. Stress–strain response of a viscoplastic material at different strain rates. The dotted lines show the response if the strain-rate is held constant. The blue line shows the response when the strain rate is changed
10219:
11441:
532:
2426:
3854:
This model is adopted when metals and alloys are at medium and higher temperatures and wood under high loads. The responses for strain hardening, creep, and relaxation tests of such a material are shown in Figure 9.
6534:
8838:
12486:
1946:
5053:
1849:
4991:
Numerous empirical and semi-empirical flow stress models are used the computational plasticity. The following temperature and strain-rate dependent models provide a sampling of the models in current use:
300:
upon application of a load and then allowed to relax back to the yield surface over time. The yield surface is usually assumed not to be rate-dependent in such models. An alternative approach is to add a
7939:
4930:
4338:
653:
619:
11818:
Levy, M. (1871), "Extrait du mémoire sur les equations générales des mouvements intérieures des corps solides ductiles au dela des limites ou l'élasticité pourrait les ramener à leur premier état",
1676:{\displaystyle {\boldsymbol {\sigma }}=\eta ~{\dot {\boldsymbol {\varepsilon }}}_{\mathrm {vp} }\implies {\dot {\boldsymbol {\varepsilon }}}_{\mathrm {vp} }={\cfrac {\boldsymbol {\sigma }}{\eta }}}
4883:
4854:
2389:
2940:
10507:
9034:
8289:
5692:
3502:
2597:
1450:
5599:{\displaystyle {\dot {\varepsilon _{\rm {p}}}}^{*}:={\cfrac {\dot {\varepsilon _{\rm {p}}}}{\dot {\varepsilon _{\rm {p0}}}}}\qquad {\text{and}}\qquad T^{*}:={\cfrac {(T-T_{0})}{(T_{m}-T_{0})}}}
1531:
6937:
509:. For a viscoplastic material the hardening curves are not significantly different from those of rate-independent plastic material. Nevertheless, three essential differences can be observed.
5647:
9884:
9750:
5347:
820:
755:
8944:
6437:
1479:
3492:
continues to increase beyond the initial yielding point. This implies that the yield stress in the sliding element increases with strain and the model may be expressed in generic terms as
7427:{\displaystyle {\text{(3)}}\qquad \sigma _{y}(\varepsilon _{\rm {p}},{\dot {\varepsilon _{\rm {p}}}},T)=\sigma _{a}+B\exp(-\beta T)+B_{0}{\sqrt {\varepsilon _{\rm {p}}}}\exp(-\alpha T)~.}
8284:
5649:
is the effective plastic strain-rate of the quasi-static test used to determine the yield and hardening parameters A,B and n. This is not as it is often thought just a parameter to make
6162:
1822:
8904:
7466:
6497:
4275:
7941:
are material parameters that depend on the type of material (fcc, bcc, hcp, alloys). The
Zerilli–Armstrong model has been modified by for better performance at high temperatures.
5305:
4384:
4572:
1330:{\displaystyle {\cfrac {\mathrm {d} {\boldsymbol {\varepsilon }}_{\mathrm {vp} }}{\mathrm {d} t}}=-{\mathsf {E}}^{-1}~{\cfrac {\mathrm {d} {\boldsymbol {\sigma }}}{\mathrm {d} t}}}
12242:
6278:
1191:{\displaystyle {\cfrac {\mathrm {d} {\boldsymbol {\varepsilon }}_{\mathrm {e} }}{\mathrm {d} t}}={\mathsf {E}}^{-1}~{\cfrac {\mathrm {d} {\boldsymbol {\sigma }}}{\mathrm {d} t}}}
11381:
11434:
11331:
11272:
4301:
2344:
2093:
12440:
Goto, D. M.; Garrett, R. K.; Bingert, J. F.; Chen, S. R.; and Gray, G. T. (2000), "The mechanical threshold stress constitutive-strength model description of HY-100 steel",
9813:
8785:
4825:
1564:
9780:
9678:
8115:{\displaystyle {\text{(4)}}\qquad \sigma _{y}(\varepsilon _{\rm {p}},{\dot {\varepsilon }},T)=\sigma _{a}+(S_{i}\sigma _{i}+S_{e}\sigma _{e}){\frac {\mu (p,T)}{\mu _{0}}}}
11205:
9648:
8934:
8243:
8203:
8176:
8149:
7578:
7459:
6930:
6886:
6527:
6309:
6189:
6124:
5046:
283:
5783:
696:
stage, also known as transient creep, is the starting stage during which hardening of the material leads to a decrease in the rate of flow which is initially very high.
11299:
11232:
10452:
10425:
10371:
7094:
6224:
5395:
437:
Symposium "Creep in
Structures" organized by Hoff provided a major development in viscoplasticity with the works of Hoff, Rabotnov, Perzyna, Hult, and Lemaitre for the
8270:
6465:
6251:
117:
10472:
9846:
7701:
7678:
9911:
7721:
6793:
4249:
11626:
10398:
8719:
7605:
7125:
6855:
6828:
5746:
5719:
4985:
4530:
4358:
2933:
2192:
1723:
1703:
7193:
11799:
5809:
2419:
465:
For a qualitative analysis, several characteristic tests are performed to describe the phenomenology of viscoplastic materials. Some examples of these tests are
12530:
Puchi-cabrera, E. S.; Villalobos-Gutierrez, C.; and Castro-Farinas, G. (2001), "On the mechanical threshold stress of aluminum: Effect of the alloying content",
11646:
10492:
8739:
7645:
7625:
7241:
7217:
7169:
7145:
6336:
4954:
4550:
1844:
141:
93:
699:
252:
6800:
2315:{\displaystyle {\boldsymbol {s}}=2K~\left({\sqrt {3}}{\dot {\varepsilon }}_{\mathrm {eq} }\right)^{m-1}~{\dot {\boldsymbol {\varepsilon }}}_{\mathrm {vp} }}
7866:{\displaystyle \alpha =\alpha _{0}-\alpha _{1}\ln({\dot {\varepsilon _{\rm {p}}}});\quad \beta =\beta _{0}-\beta _{1}\ln({\dot {\varepsilon _{\rm {p}}}});}
4496:{\displaystyle {\dot {\varepsilon }}_{\mathrm {vp} }=\left\langle {\frac {f}{f_{0}}}\right\rangle ^{n}sign({\boldsymbol {\sigma }}-{\boldsymbol {\chi }})}
1346:
2392:
7148:
8178:
is the component of the flow stress due to intrinsic barriers to thermally activated dislocation motion and dislocation-dislocation interactions,
4956:
is often expressed as an equation consisting of some invariant of stress and a model for the yield stress (or plastic flow stress). An example is
4856:
is the closest point projection of the stress state on to the boundary of the region that bounds all possible elastic stress states. The quantity
12532:
11763:
445:
laws. Perzyna, in 1963, introduced a viscosity coefficient that is temperature and time dependent. The formulated models were supported by the
527:
The hypothesis of partitioning the strains by decoupling the elastic and plastic parts is still applicable where the strains are small, i.e.,
888:
Figure 4. a) Applied strain in a relaxation test and b) induced stress as functions of time over a short period for a viscoplastic material.
8790:
12685:
Abed, F. H. and
Voyiadjis, G. Z. (2005), "A consistent modified Zerilli–Armstrong flow stress model for BCC and FCC metals for elevated",
11761:
Batra, R. C. and Kim, C. H. (1990), "Effect of viscoplastic flow rules on the initiation and growth of shear bands at high strain rates",
10337:{\displaystyle \alpha :={\frac {s_{0}-\tau _{y}}{d}};\quad \beta :={\frac {\tau _{s}-\tau _{y}}{\alpha }};\quad \varphi :=\exp(\beta )-1}
6796:
893:
used to determine the relation which exists between the stress and the rate of viscoplastic strain. The decomposition of strain rate is
7255:
The
Zerilli–Armstrong (ZA) model is based on simplified dislocation mechanics. The general form of the equation for the flow stress is
1934:{\displaystyle ||{\boldsymbol {\sigma }}||={\sqrt {{\boldsymbol {\sigma }}:{\boldsymbol {\sigma }}}}={\sqrt {\sigma _{ij}\sigma _{ij}}}}
12442:
12398:
8937:
11599:{\displaystyle {\dot {\xi }}={\frac {1}{2}}\left({\cfrac {4\pi \rho }{3M}}\right)^{1/3}\left({\cfrac {\mu (p,T)}{\rho }}\right)^{1/2}}
581:{\displaystyle {\boldsymbol {\varepsilon }}={\boldsymbol {\varepsilon }}_{\mathrm {e} }+{\boldsymbol {\varepsilon }}_{\mathrm {vp} }}
6343:
12165:
7878:
2524:{\displaystyle {\dot {\bar {\epsilon }}}={\sqrt {{\frac {2}{3}}{\dot {\bar {\bar {\epsilon }}}}:{\dot {\bar {\bar {\epsilon }}}}}}}
4896:
4309:
624:
12601:
593:
6756:{\displaystyle {\dot {\varepsilon _{\rm {p}}}}=\left+{\frac {C_{2}}{\sigma _{t}}}\right]^{-1};\quad \sigma _{t}\leq \sigma _{p}}
457:
standpoint. The ideas presented in these works have been the basis for most subsequent research into rate-dependent plasticity.
1730:
12195:
Steinberg, D. J.; Cochran, S. G.; and Guinan, M. W. (1980), "A constitutive model for metals applicable at high-strain rate",
11968:
Hohenemser, K. and Prager, W. (1932), "Fundamental equations and definitions concerning the mechanics of isotropic continua",
305:
dependence to the yield stress and use the techniques of rate independent plasticity to calculate the response of a material.
12139:
5308:
4859:
4830:
2353:
5652:
2079:{\displaystyle {\dot {\boldsymbol {\varepsilon }}}_{\mathrm {vp} }={\cfrac {\boldsymbol {\sigma }}{\lambda }}\left^{N-1}}
1426:
5269:{\displaystyle {\text{(1)}}\qquad \sigma _{y}(\varepsilon _{\rm {p}},{\dot {\varepsilon _{\rm {p}}}},T)=\left\left\left}
1501:
868:{\displaystyle ({\boldsymbol {\varepsilon }}_{2}\leq {\boldsymbol {\varepsilon }}\leq {\boldsymbol {\varepsilon }}_{R})}
803:{\displaystyle ({\boldsymbol {\varepsilon }}_{1}\leq {\boldsymbol {\varepsilon }}\leq {\boldsymbol {\varepsilon }}_{2})}
12270:
Hoge, K. G. and
Mukherjee, A. K. (1977), "The temperature and strain rate dependence of the flow stress of tantalum",
8205:
is the component of the flow stress due to microstructural evolution with increasing deformation (strain hardening), (
5611:
9851:
9683:
5314:
410:
Concepts such as the normality of plastic flow to the yield surface and flow rules for plasticity were introduced by
296:
of the
Perzyna or Duvaut-Lions types. In these models, the stress is allowed to increase beyond the rate-independent
1455:
1343:
It is important to note that relaxation tests are extremely difficult to perform because maintaining the condition
3891:
In the Perzyna formulation the plastic strain rate is assumed to be given by a constitutive relation of the form
6129:
36:
that describes the rate-dependent inelastic behavior of solids. Rate-dependence in this context means that the
12789:
8843:
6470:
4258:
3063:{\displaystyle {\cfrac {\boldsymbol {\sigma }}{\eta }}={\cfrac {\boldsymbol {\sigma }}{\lambda }}\left^{N-1}}
12613:
Zerilli, F. J. and Armstrong, R. W. (1994), "Constitutive relations for the plastic deformation of metals",
5281:
4363:
430:
However, the application of these theories did not begin before 1950, where limit theorems were discovered.
399:. In viscoplasticity, the development of a mathematical model heads back to 1910 with the representation of
12784:
12272:
4555:
2935:
is the viscosity of the dashpot element. If the dashpot element has a response that is of the Norton form
7060:{\displaystyle C_{1}:={\frac {\rho _{d}L_{d}ab^{2}\nu }{2w^{2}}};\quad C_{2}:={\frac {D}{\rho _{d}b^{2}}}}
6256:
6253:
is the shear modulus at standard temperature and pressure. The saturation value of the athermal stress is
3872:
516:
A change in the rate of strain during the test results in an immediate change in the stress–strain curve.
11336:
3478:
Figure 8. The response of elastic perfectly viscoplastic solid to hardening, creep and relaxation tests.
3471:
The responses for strain hardening, creep, and relaxation tests of such material are shown in Figure 8.
12567:
12323:
12197:
11386:
11304:
11237:
9015:{\displaystyle {\text{(5)}}\qquad {\frac {d\sigma _{e}}{d\varepsilon _{\rm {p}}}}=\theta (\sigma _{e})}
5021:
The Johnson–Cook (JC) model is purely empirical and gives the following relation for the flow stress (
4284:
2327:
12362:"A constitutive description of the deformation of copper based on the use of the mechanical threshold"
3862:
Figure 9. The response of elastoviscoplastic hardening solid to hardening, creep and relaxation tests.
12484:
Banerjee, B. (2007), "The mechanical threshold stress model for various tempers of AISI 4340 steel",
4957:
403:
by Andrade's law. In 1929, Norton developed a one-dimensional dashpot model which linked the rate of
396:
10003:
8685:{\displaystyle {\begin{aligned}S_{i}&=\left^{1/p_{i}}\\S_{e}&=\left^{1/p_{e}}\end{aligned}}}
4631:
4028:
11854:
Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse
9785:
8744:
4806:
3326:
Other expressions for the strain rate can also be observed in the literature with the general form
1536:
340:, the theory of viscoplasticity is required to describe behavior beyond the limit of elasticity or
9755:
9653:
2575:. In the second situation, all three elements are arranged in parallel. Such a model is called a
388:
12166:"A constitutive model and data for metals subjected to large strains, high strain rates and high"
11183:
9626:
8912:
8208:
8181:
8154:
8127:
7556:
7437:
6895:
6864:
6505:
6287:
6167:
6102:
5024:
418:
proposed the first model for slow viscoplastic flow. This model provided a relation between the
261:
37:
7544:{\displaystyle \sigma _{a}:=\sigma _{g}+{\frac {k_{h}}{\sqrt {l}}}+K\varepsilon _{\rm {p}}^{n},}
5755:
441:
laws, and those of Kratochvil, Malinini and Khadjinsky, Ponter and Leckie, and Chaboche for the
11277:
11210:
10430:
10403:
10349:
7072:
6194:
5356:
2541:
Figure 6: The response of perfectly viscoplastic solid to hardening, creep and relaxation tests
454:
12602:
http://www.dynalook.com/european-conf-2007/optional-strain-rate-forms-for-the-johnson-cook.pdf
11934:
Reuss, A. (1930), "Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie",
8248:
6444:
6229:
4590:
The Duvaut–Lions formulation is equivalent to the Perzyna formulation and may be expressed as
102:
10457:
9818:
7686:
7650:
1200:
For the flat region of the strain–time curve, the total strain rate is zero. Hence we have,
9889:
7706:
6768:
4219:
660:) but not by models of rate-independent plasticity that have a rate-dependent yield stress.
12622:
12576:
12451:
12407:
12332:
12281:
12206:
11977:
11943:
11772:
11677:
11611:
10376:
8697:
7583:
7103:
6833:
6806:
5724:
5697:
4963:
4508:
4343:
2918:
2171:
1708:
1688:
502:
450:
45:
9886:
is the maximum strain-rate. Note that the maximum strain-rate is usually limited to about
7178:
8:
11682:
11672:
5788:
2398:
2159:{\displaystyle \sigma =\lambda ~\left({\dot {\varepsilon }}_{\mathrm {vp} }\right)^{1/N}}
738:{\displaystyle (0\leq {\boldsymbol {\varepsilon }}\leq {\boldsymbol {\varepsilon }}_{1})}
684:
520:
494:
404:
400:
255:
50:
33:
12626:
12580:
12455:
12411:
12336:
12285:
12210:
12066:, vol. II: Viscoplasticity, Damage, Fracture and Contact Mechanics, Kluwer Academic
11981:
11947:
11776:
2205:(volume preserving), then the above relation can be expressed in the more familiar form
12702:
12668:
12513:
12495:
12467:
12423:
12319:"Dislocation-mechanics-based constitutive relations for material dynamics calculations"
12297:
11797:
Tresca, H. (1864), "Sur l'Ă©coulement des Corps solides soumis Ă des fortes pressions",
11631:
10477:
8724:
8276:
7630:
7610:
7226:
7202:
7154:
7130:
6858:
6321:
4939:
4535:
4278:
1829:
498:
126:
96:
78:
12766:
12736:
150:
56:
The elastic response of viscoplastic materials can be represented in one-dimension by
12706:
12672:
12471:
12427:
12379:
12366:
12301:
12135:
11852:
von Mises, R. (1913), "Mechanik der festen Körper im plastisch deformablen Zustand",
11784:
4387:
2347:
2202:
1420:
419:
363:
systems exposed to high temperatures such as turbines in engines, e.g. a power plant,
1399:{\displaystyle {\cfrac {\mathrm {d} {\boldsymbol {\varepsilon }}}{\mathrm {d} t}}=0}
12762:
12732:
12694:
12660:
12630:
12584:
12541:
12517:
12509:
12505:
12459:
12415:
12375:
12340:
12289:
12214:
11985:
11951:
11780:
7244:
3488:
2564:
817:
phase in which there is an increase in the strain rate up to the fracture strain.
407:
to the stress. In 1934, Odqvist generalized Norton's law to the multi-axial case.
12129:
11662:
11657:
7196:
2568:
1416:
427:
341:
68:
60:
41:
384:
49:
permanent deformations after the application of loads but continue to undergo a
12529:
11917:
7220:
7172:
6889:
6281:
4885:
is typically found from the rate-independent solution to a plasticity problem.
4304:
506:
446:
442:
438:
415:
57:
12698:
12664:
12463:
2545:
44:
are applied. The inelastic behavior that is the subject of viscoplasticity is
12778:
11955:
6312:
5749:
4933:
4252:
752:
stage, also known as the steady state, is where the strain rate is constant.
297:
10494:
is a dimensionless material parameter that modifies the Voce hardening law.
25:
Figure 1. Elements used in one-dimensional models of viscoplastic materials.
5400:
The normalized strain-rate and temperature in equation (1) are defined as
2580:
2195:
380:
376:
12721:"Anisotropy-corrected MTS constitutive strength modeling in HY-100 steel"
12500:
11922:
Proceedings of the 1st International Congress on Applied Mechanics, Delft
11687:
7097:
5350:
1846:
is a fitting parameter, λ is the kinematic viscosity of the material and
1705:
is the viscosity of the dashpot. In the Norton-Hoff model the viscosity
423:
325:
321:
317:
302:
286:
12719:
Goto, D. M.; Bingert, J. F.; Reed, W. R.; and Garrett Jr, R. K. (2000),
12237:
7683:
In the thermally activated terms, the functional forms of the exponents
21:
12419:
12293:
6529:) is computed using a bisection algorithm from the following equation.
3474:
513:
At the same strain, the higher the rate of strain the higher the stress
12588:
12545:
11989:
11904:
Proceedings of the Fourth International Congress for Applied Mechanics
2587:
is exceeded irrespective of the strain. The model can be expressed as
12344:
12218:
8833:{\displaystyle {\dot {\varepsilon }},{\dot {\varepsilon _{\rm {0}}}}}
392:
144:
120:
12750:
12720:
12648:
12634:
12562:
12393:
12361:
12318:
7580:
is the contribution due to solutes and initial dislocation density,
53:
flow as a function of time under the influence of the applied load.
8909:
The strain hardening component of the mechanical threshold stress (
2088:
In one-dimensional form, the Norton-Hoff model can be expressed as
1484:
72:
8245:) are temperature and strain-rate dependent scaling factors, and
5814:
2421:
are material parameters. The equivalent strain rate is defined as
347:
In general, viscoplasticity theories are useful in areas such as:
11667:
6311:). The shear modulus for this model is usually computed with the
411:
375:
Research on plasticity theories started in 1864 with the work of
337:
329:
64:
12394:"Constitutive behavior of tantalum and tantalum-tungsten alloys"
9815:
is the saturation threshold stress for deformation at 0 K,
7944:
4394:
model is a special case of Perzyna's flow rule and has the form
11902:
Odqvist, F. K. G. (1934), "Creep stresses in a rotating disc",
11706:
Perzyna, P. (1966), "Fundamental problems in viscoplasticity",
11436:) are material parameters for the high strain-rate regime, and
3858:
2537:
6226:
is the pressure- and temperature-dependent shear modulus, and
1941:. Then the viscoplastic strain rate is given by the relation
1725:
is a nonlinear function of the applied stress and is given by
676:
12563:"Model of plastic deformation for extreme loading conditions"
7934:{\displaystyle \alpha _{0},\alpha _{1},\beta _{0},\beta _{1}}
884:
668:
434:
313:
309:
292:
Viscoplasticity is usually modeled in three-dimensions using
12173:
Proceedings of the 7th International Symposium on Ballistics
4925:{\displaystyle f({\boldsymbol {\sigma }},{\boldsymbol {q}})}
4333:{\displaystyle {\boldsymbol {\varepsilon }}_{\mathrm {vp} }}
1493:
Figure 5. Norton-Hoff model for perfectly viscoplastic solid
648:{\displaystyle {\boldsymbol {\varepsilon }}_{\mathrm {vp} }}
10198:
6280:. The saturation of the thermally activated stress is the
4787:
4200:
2546:
Elastic perfectly viscoplastic solid (Bingham–Norton model)
614:{\displaystyle {\boldsymbol {\varepsilon }}_{\mathrm {e} }}
333:
63:
elements. Rate-dependence can be represented by nonlinear
9916:
8151:
is the athermal component of mechanical threshold stress,
7949:
The Mechanical Threshold Stress (MTS) model) has the form
3866:
2550:
1489:
484:
366:
dynamic problems and systems exposed to high strain rates.
12718:
12561:
Preston, D. L.; Tonks, D. L.; and Wallace, D. C. (2003),
12049:
The Science and Technology of Civil Engineering Materials
10474:
is the hardening constant in the Voce hardening law, and
6191:
is the thermally activated component of the flow stress,
391:. An improved plasticity model was presented in 1913 by
320:
behavior caused by a mechanism linked to the movement of
10497:
The saturation stress and the yield stress are given by
4578:. Several models for the backstress also go by the name
1409:
497:
is that as plastic deformation proceeds, an increase in
12751:"Realistic constitutive relations for metal plasticity"
12238:"A constitutive model for strain rates from 10 to 10 s"
12097:
Numerical Modeling in Materials Science and Engineering
12046:
11565:
11538:
11496:
11478:
11110:
11082:
11019:
10991:
10924:
10900:
10734:
10706:
10647:
10623:
10097:
10073:
9574:
9546:
9431:
9409:
9368:
9336:
9317:
9295:
5557:
5526:
5471:
5443:
4686:
4657:
4096:
4081:
4065:
4034:
4002:
3987:
3971:
3930:
3249:
3230:
3187:
3167:
3146:
3134:
3031:
3011:
2990:
2978:
2959:
2947:
2832:
2813:
2786:
2774:
2047:
2013:
1992:
1980:
1763:
1751:
1660:
1648:
1372:
1353:
1309:
1290:
1243:
1212:
1170:
1151:
1107:
1079:
1031:
1000:
976:
948:
924:
905:
680:
Figure 3b. Strain as a function of time in a creep test
12439:
12194:
11568:
11541:
11499:
11481:
11113:
11085:
11022:
10994:
10927:
10903:
10737:
10709:
10650:
10626:
10100:
10076:
9577:
9549:
9434:
9412:
9371:
9339:
9320:
9298:
8840:) are the strain-rate and reference strain-rate, and (
7461:
is the athermal component of the flow stress given by
7250:
5560:
5529:
5474:
5446:
4689:
4660:
4099:
4084:
4068:
4037:
4005:
3990:
3974:
3933:
3871:
Classical phenomenological viscoplasticity models for
3252:
3233:
3190:
3170:
3149:
3137:
3034:
3014:
2993:
2981:
2962:
2950:
2835:
2816:
2789:
2777:
2554:
Figure 7. The elastic perfectly viscoplastic material.
2050:
2016:
1995:
1983:
1766:
1754:
1663:
1651:
1375:
1356:
1312:
1293:
1246:
1215:
1173:
1154:
1110:
1082:
1034:
1003:
979:
951:
927:
908:
11634:
11614:
11444:
11389:
11339:
11307:
11280:
11240:
11213:
11186:
10505:
10480:
10460:
10433:
10406:
10379:
10352:
10222:
9930:
9892:
9854:
9821:
9788:
9758:
9686:
9656:
9629:
9032:
8947:
8915:
8846:
8793:
8747:
8727:
8700:
8287:
8251:
8211:
8184:
8157:
8130:
7957:
7881:
7731:
7709:
7689:
7653:
7633:
7613:
7586:
7559:
7469:
7440:
7263:
7229:
7205:
7181:
7157:
7133:
7106:
7075:
6940:
6898:
6867:
6836:
6809:
6771:
6537:
6508:
6473:
6447:
6346:
6324:
6290:
6259:
6232:
6197:
6170:
6132:
6105:
5828:
5791:
5758:
5727:
5700:
5655:
5614:
5408:
5359:
5317:
5284:
5056:
5027:
4966:
4942:
4899:
4878:{\displaystyle {\mathcal {P}}{\boldsymbol {\sigma }}}
4862:
4849:{\displaystyle {\mathcal {P}}{\boldsymbol {\sigma }}}
4833:
4809:
4598:
4558:
4538:
4511:
4402:
4366:
4346:
4312:
4287:
4261:
4222:
3899:
3500:
3482:
3334:
3080:
2943:
2921:
2595:
2429:
2401:
2384:{\displaystyle {\dot {\varepsilon }}_{\mathrm {eq} }}
2356:
2330:
2213:
2174:
2096:
1949:
1852:
1832:
1733:
1711:
1691:
1574:
1539:
1504:
1458:
1429:
1349:
1208:
1075:
901:
823:
758:
702:
627:
596:
535:
354:
the prediction of the plastic collapse of structures,
264:
153:
129:
105:
81:
71:. Plasticity can be accounted for by adding sliding
12649:"Dislocation mechanics-based constitutive equations"
289:
dependent, or even constant, as shown in Figure 1c.
12560:
12094:
12061:
5687:{\displaystyle {\dot {\varepsilon _{\rm {p}}}}^{*}}
1445:{\displaystyle {\dot {\boldsymbol {\varepsilon }}}}
11936:Zeitschrift fĂĽr Angewandte Mathematik und Mechanik
11800:Comptes Rendus de l'Académie des Sciences de Paris
11640:
11620:
11598:
11428:
11375:
11325:
11293:
11266:
11226:
11199:
11170:
10486:
10466:
10446:
10419:
10392:
10373:is a normalized work-hardening saturation stress,
10365:
10336:
10204:
9905:
9878:
9840:
9807:
9774:
9744:
9672:
9650:is the hardening due to dislocation accumulation,
9642:
9613:
9014:
8928:
8898:
8832:
8779:
8733:
8713:
8684:
8272:is the shear modulus at 0 K and ambient pressure.
8264:
8237:
8197:
8170:
8143:
8114:
7933:
7865:
7715:
7695:
7672:
7639:
7619:
7599:
7572:
7543:
7453:
7426:
7235:
7211:
7187:
7163:
7139:
7119:
7088:
7059:
6924:
6880:
6849:
6822:
6787:
6755:
6521:
6491:
6459:
6431:
6330:
6303:
6272:
6245:
6218:
6183:
6156:
6118:
6089:
5803:
5777:
5740:
5713:
5686:
5641:
5598:
5389:
5341:
5299:
5268:
5040:
4979:
4948:
4924:
4877:
4848:
4819:
4793:
4566:
4544:
4524:
4495:
4378:
4352:
4332:
4295:
4269:
4243:
4206:
3844:
3461:
3316:
3062:
2927:
2905:
2523:
2413:
2383:
2338:
2314:
2186:
2158:
2078:
1933:
1838:
1816:
1717:
1697:
1675:
1558:
1533:and hence there is no initial yield stress, i.e.,
1526:{\displaystyle {\boldsymbol {\varepsilon }}_{e}=0}
1525:
1473:
1444:
1398:
1329:
1190:
1057:
867:
802:
737:
647:
613:
580:
469:hardening tests at constant stress or strain rate,
277:
246:
147:type parameter that represents non-linear dashpot
135:
111:
87:
5016:
414:(1924) and Reuss (1930). In 1932, Hohenemser and
12776:
12612:
12316:
12095:Rappaz, M.; Bellet, M.; and Deville, M. (1998),
12062:François, D.; Pineau, A.; and Zaoui, A. (1993),
11967:
11724:
10965:
10804:
10527:
9680:is the contribution due to stage-IV hardening, (
6164:is a function that represents strain hardening,
5642:{\displaystyle {\dot {\varepsilon _{\rm {p0}}}}}
4390:. The flow rule used in various versions of the
1485:Perfectly viscoplastic solid (Norton-Hoff model)
1067:The elastic part of the strain rate is given by
12533:Journal of Engineering Materials and Technology
12359:
9879:{\displaystyle {\dot {\varepsilon _{\rm {p}}}}}
9745:{\displaystyle a_{0},a_{1},a_{2},a_{3},\alpha }
5815:Steinberg–Cochran–Guinan–Lund flow stress model
5342:{\displaystyle {\dot {\varepsilon _{\rm {p}}}}}
1566:. The viscous dashpot has a response given by
12487:International Journal of Solids and Structures
12231:
12229:
12227:
12190:
12188:
12081:, International Centre for Mechanical Sciences
12076:
11764:Journal of the Mechanics and Physics of Solids
6432:{\displaystyle f(\varepsilon _{\rm {p}})=^{n}}
6126:is the athermal component of the flow stress,
1474:{\displaystyle {\dot {\boldsymbol {\sigma }}}}
12684:
12269:
12235:
9782:is the stress at zero strain hardening rate,
7945:Mechanical threshold stress flow stress model
75:elements as shown in Figure 1. In the figure
40:of the material depends on the rate at which
12556:
12554:
12355:
12353:
12317:Zerilli, F. J. and Armstrong, R. W. (1987),
12312:
12310:
12159:
12157:
12121:
11820:Journal de Mathématiques Pures et Appliquées
6313:Steinberg–Cochran–Guinan shear modulus model
4373:
4367:
4303:is a set of internal variables (such as the
3443:
3435:
3298:
3290:
3262:
3254:
3180:
3172:
3024:
3016:
2883:
2875:
2845:
2837:
2649:
2641:
12477:
12360:Follansbee, P. S. and Kocks, U. F. (1988),
12224:
12185:
12163:
11839:Inelastic Analysis of Solids and Structures
4585:
12653:Metallurgical and Materials Transactions A
12443:Metallurgical and Materials Transactions A
12399:Metallurgical and Materials Transactions A
12047:Young; Mindness; Gray; and Bentur (1998),
11836:
11746:
8741:is the magnitude of the Burgers' vector, (
6499:is the initial equivalent plastic strain.
1617:
1613:
1406:in a test requires considerable delicacy.
351:the calculation of permanent deformations,
12640:
12606:
12551:
12499:
12350:
12307:
12265:
12263:
12236:Steinberg, D. J. and Lund, C. M. (1988),
12154:
12108:
12106:
12090:
12088:
12070:
12019:IUTAM Colloquium Creep in Structures; 1st
11851:
11747:Simo, J. C. and Hughes, T. J. R. (1998),
11725:Lemaître, J. and Chaboche, J. L. (2002),
7607:is the microstructural stress intensity,
6157:{\displaystyle f(\varepsilon _{\rm {p}})}
1817:{\displaystyle \eta =\lambda \left^{N-1}}
475:stress relaxation at constant elongation.
12483:
12391:
12127:
12055:
12031:
11867:
11865:
11863:
11760:
11301:at 0 K and close to melt, respectively,
7127:is the length of a dislocation segment,
4999:the Steinberg–Cochran–Guinan–Lund model.
3875:are usually categorized into two types:
3857:
3473:
2549:
2536:
1488:
883:
675:
667:
657:
483:
479:
20:
12742:
12712:
12646:
12523:
12164:Johnson, G. R. and Cook, W. H. (1983),
12001:
11995:
11916:
11910:
11901:
11895:
11705:
9917:Preston–Tonks–Wallace flow stress model
8899:{\displaystyle q_{i},p_{i},q_{e},p_{e}}
8787:) are normalized activation energies, (
6492:{\displaystyle \varepsilon _{\rm {p}}i}
4915:
4907:
4871:
4842:
4729:
4721:
4678:
4663:
4560:
4486:
4478:
4315:
4289:
4270:{\displaystyle {\boldsymbol {\sigma }}}
4263:
4144:
4136:
4105:
4054:
4046:
4011:
3955:
3947:
3867:Strain-rate dependent plasticity models
3811:
3779:
3757:
3735:
3716:
3670:
3646:
3630:
3595:
3563:
3552:
3516:
3507:
3439:
3416:
3392:
3373:
3338:
3294:
3258:
3176:
3139:
3119:
3084:
3020:
2983:
2952:
2879:
2841:
2779:
2759:
2713:
2689:
2673:
2645:
2620:
2602:
2332:
2292:
2215:
2029:
1985:
1954:
1892:
1884:
1864:
1779:
1653:
1622:
1593:
1576:
1507:
1462:
1433:
1364:
1301:
1224:
1162:
1091:
1012:
960:
916:
852:
843:
829:
787:
778:
764:
722:
713:
630:
599:
563:
546:
537:
12777:
12678:
12433:
12385:
12260:
12112:
12103:
12085:
12079:Viscoplastic Behaviour of Geomaterials
11886:
11880:
11871:
11796:
11742:
11740:
11738:
11736:
11699:
5300:{\displaystyle \varepsilon _{\rm {p}}}
5005:the Mechanical threshold stress model.
4812:
4637:
4379:{\displaystyle \langle \dots \rangle }
3886:
3696:
3534:
3487:An elastic-viscoplastic material with
3353:
3099:
2739:
2611:
1270:
1131:
12748:
11961:
11933:
11927:
11860:
11790:
4888:
4567:{\displaystyle {\boldsymbol {\chi }}}
1410:Rheological models of viscoplasticity
12755:Materials Science and Engineering: A
12392:Chen, S. R. and Gray, G. T. (1996),
12077:Cristescu, N. and Gioda, G. (1994),
12016:
12010:
11845:
11830:
11817:
11754:
8936:) is given by an empirical modified
6273:{\displaystyle \sigma _{\text{max}}}
11889:Creep of steel at high temperatures
11811:
11733:
7251:Zerilli–Armstrong flow stress model
6467:are work hardening parameters, and
4360:is a relaxation time. The notation
13:
11837:Kojic, M. and Bathe, K-J. (2006),
11376:{\displaystyle {\hat {T}}=T/T_{m}}
11259:
11192:
11141:
11095:
11065:
11050:
11004:
10974:
10937:
10878:
10863:
10860:
10857:
10846:
10765:
10719:
10689:
10660:
10601:
10586:
10583:
10580:
10569:
10087:
9974:
9956:
9864:
9587:
9559:
9233:
9198:
8981:
7983:
7845:
7779:
7527:
7389:
7307:
7289:
6547:
6480:
6407:
6392:
6359:
6145:
5957:
5923:
5872:
5854:
5666:
5624:
5484:
5456:
5419:
5327:
5291:
5201:
5147:
5100:
5082:
4865:
4836:
4779:
4776:
4773:
4770:
4767:
4764:
4761:
4758:
4755:
4714:
4707:
4704:
4672:
4617:
4614:
4421:
4418:
4324:
4321:
4192:
4189:
4186:
4183:
4180:
4177:
4174:
4171:
4168:
4121:
4118:
4101:
4086:
4007:
3992:
3918:
3915:
3793:
3790:
3787:
3766:
3763:
3684:
3681:
3657:
3577:
3574:
3571:
3522:
3483:Elastoviscoplastic hardening solid
3428:
3425:
3422:
3283:
3280:
3277:
2868:
2865:
2862:
2727:
2724:
2700:
2634:
2631:
2628:
2375:
2372:
2306:
2303:
2262:
2259:
2201:If we assume that plastic flow is
2132:
2129:
1968:
1965:
1636:
1633:
1607:
1604:
1378:
1359:
1315:
1296:
1249:
1233:
1230:
1218:
1176:
1157:
1113:
1097:
1085:
1037:
1021:
1018:
1006:
982:
966:
954:
930:
911:
879:
639:
636:
605:
572:
569:
552:
501:is required to produce additional
472:creep tests at constant force, and
216:
203:
177:
164:
14:
12801:
12064:Mechanical Behaviour of Materials
11429:{\displaystyle s_{1},y_{1},y_{2}}
11326:{\displaystyle (\kappa ,\gamma )}
11267:{\displaystyle y_{0},y_{\infty }}
4827:is the elastic stiffness tensor,
4296:{\displaystyle {\boldsymbol {q}}}
2339:{\displaystyle {\boldsymbol {s}}}
523:is no longer strictly applicable.
254:. The sliding element can have a
11234:close to the melt temperature, (
5721:is a reference temperature, and
5008:the Preston–Tonks–Wallace model.
4932:represents the evolution of the
3072:we get the Bingham–Norton model
460:
395:which is now referred to as the
67:elements in a manner similar to
12594:
12040:
12025:
10306:
10264:
9936:
8953:
7963:
7797:
7627:is the average grain diameter,
7269:
7014:
6729:
6318:The strain hardening function (
6020:
5834:
5509:
5503:
5062:
3420:
3275:
357:the investigation of stability,
12510:10.1016/j.ijsolstr.2006.05.022
12243:Journal de Physique. Colloques
11718:
11558:
11546:
11346:
11320:
11308:
10881:
10851:
10825:
10604:
10574:
10548:
10454:is a normalized yield stress,
10325:
10319:
10185:
10173:
10143:
10131:
9992:
9947:
9523:
9511:
9457:
9403:
9385:
9379:
9282:
9269:
9136:
9123:
9101:
9098:
9085:
9073:
9053:
9040:
9009:
8996:
8581:
8569:
8386:
8374:
8096:
8084:
8075:
8029:
8010:
7974:
7857:
7833:
7791:
7767:
7415:
7403:
7365:
7353:
7325:
7280:
6420:
6416:
6383:
6371:
6365:
6350:
6213:
6201:
6151:
6136:
6001:
5989:
5975:
5945:
5929:
5914:
5890:
5845:
5588:
5562:
5550:
5531:
5252:
5238:
5219:
5188:
5154:
5138:
5118:
5073:
5017:Johnson–Cook flow stress model
4919:
4903:
4733:
4717:
4490:
4474:
4238:
4226:
4148:
4132:
4058:
4042:
3959:
3943:
3821:
3816:
3806:
3801:
3772:
3731:
3605:
3600:
3590:
3585:
3409:
3388:
2508:
2503:
2479:
2474:
2438:
2039:
2034:
2024:
2019:
1874:
1869:
1859:
1854:
1789:
1784:
1774:
1769:
1614:
862:
824:
797:
759:
732:
703:
505:. This phenomenon is known as
241:
224:
199:
184:
160:
154:
1:
12767:10.1016/S0921-5093(01)01174-1
12737:10.1016/S1359-6462(00)00347-X
11708:Advances in Applied Mechanics
11693:
9808:{\displaystyle \sigma _{0es}}
8780:{\displaystyle g_{0i},g_{0e}}
8275:The scaling factors take the
4820:{\displaystyle {\mathsf {C}}}
1559:{\displaystyle \sigma _{y}=0}
663:
16:Theory in continuum mechanics
12380:10.1016/0001-6160(88)90030-2
12273:Journal of Materials Science
11785:10.1016/0022-5096(90)90043-4
11729:, Cambridge University Press
11727:Mechanics of solid materials
9775:{\displaystyle \sigma _{es}}
9673:{\displaystyle \theta _{IV}}
5002:the Zerilli–Armstrong model.
4532:is the quasistatic value of
3882:the Duvaut–Lions formulation
7:
12051:, New Jersey: Prentice Hall
11651:
11200:{\displaystyle s_{\infty }}
9643:{\displaystyle \theta _{0}}
8929:{\displaystyle \sigma _{e}}
8721:is the Boltzmann constant,
8238:{\displaystyle S_{i},S_{e}}
8198:{\displaystyle \sigma _{e}}
8171:{\displaystyle \sigma _{i}}
8144:{\displaystyle \sigma _{a}}
7647:is zero for fcc materials,
7573:{\displaystyle \sigma _{g}}
7454:{\displaystyle \sigma _{a}}
6932:are given by the relations
6925:{\displaystyle C_{1},C_{2}}
6881:{\displaystyle \sigma _{p}}
6522:{\displaystyle \sigma _{t}}
6304:{\displaystyle \sigma _{p}}
6184:{\displaystyle \sigma _{t}}
6119:{\displaystyle \sigma _{a}}
5041:{\displaystyle \sigma _{y}}
2393:von Mises equivalent strain
278:{\displaystyle \sigma _{y}}
10:
12806:
12615:AIP Conference Proceedings
12568:Journal of Applied Physics
12324:Journal of Applied Physics
12198:Journal of Applied Physics
11749:Computational inelasticity
5778:{\displaystyle T^{*}<0}
621:is the elastic strain and
370:
12699:10.1007/s00707-004-0203-1
12665:10.1007/s11661-004-0201-x
12464:10.1007/s11661-000-0226-8
11294:{\displaystyle \tau _{y}}
11227:{\displaystyle \tau _{s}}
10447:{\displaystyle \tau _{y}}
10420:{\displaystyle \tau _{s}}
10366:{\displaystyle \tau _{s}}
7089:{\displaystyle \rho _{d}}
6219:{\displaystyle \mu (p,T)}
5390:{\displaystyle A,B,C,n,m}
5309:equivalent plastic strain
397:von Mises yield criterion
316:, viscoplasticity is the
12128:Lubliner, Jacob (1990),
11956:10.1002/zamm.19300100308
11876:(2nd ed.), Springer
11333:are material constants,
8265:{\displaystyle \mu _{0}}
7680:are material constants.
7171:is the magnitude of the
7147:is the distance between
6795:is the energy to form a
6460:{\displaystyle \beta ,n}
6246:{\displaystyle \mu _{0}}
5397:are material constants.
4586:Duvaut–Lions formulation
112:{\displaystyle \lambda }
12647:Zerilli, F. J. (2004),
12006:, New York: McGraw-Hill
12004:Fluidity and plasticity
12002:Bingham, E. C. (1922),
11891:, New York: McGraw-Hill
10467:{\displaystyle \theta }
9841:{\displaystyle g_{0es}}
7696:{\displaystyle \alpha }
7673:{\displaystyle B,B_{0}}
6502:The thermal component (
5752:. For conditions where
4936:. The yield function
3879:the Perzyna formulation
389:maximum shear criterion
11887:Norton, F. H. (1929),
11642:
11622:
11600:
11430:
11377:
11327:
11295:
11268:
11228:
11201:
11172:
10488:
10468:
10448:
10421:
10394:
10367:
10338:
10206:
9907:
9906:{\displaystyle 10^{7}}
9880:
9842:
9809:
9776:
9746:
9674:
9644:
9615:
9016:
8930:
8900:
8834:
8781:
8735:
8715:
8686:
8266:
8239:
8199:
8172:
8145:
8116:
7935:
7867:
7717:
7716:{\displaystyle \beta }
7697:
7674:
7641:
7621:
7601:
7574:
7545:
7455:
7428:
7237:
7213:
7189:
7165:
7141:
7121:
7090:
7061:
6926:
6882:
6851:
6824:
6789:
6788:{\displaystyle 2U_{k}}
6757:
6523:
6493:
6461:
6433:
6332:
6305:
6274:
6247:
6220:
6185:
6158:
6120:
6091:
5805:
5779:
5742:
5715:
5688:
5643:
5600:
5391:
5343:
5301:
5270:
5042:
4996:the Johnson–Cook model
4981:
4950:
4926:
4879:
4850:
4821:
4795:
4568:
4546:
4526:
4497:
4380:
4354:
4334:
4297:
4271:
4245:
4244:{\displaystyle f(.,.)}
4208:
3863:
3846:
3479:
3463:
3318:
3064:
2929:
2907:
2555:
2542:
2525:
2415:
2385:
2340:
2316:
2188:
2160:
2080:
1935:
1840:
1818:
1719:
1699:
1677:
1560:
1527:
1494:
1475:
1446:
1400:
1331:
1192:
1059:
889:
869:
804:
739:
681:
673:
649:
615:
582:
490:
451:irreversible processes
426:for an incompressible
279:
248:
137:
113:
89:
26:
12749:Kocks, U. F. (2001),
12036:, New York: Macmillan
12032:Lubliner, J. (1990),
11643:
11623:
11621:{\displaystyle \rho }
11601:
11431:
11378:
11328:
11296:
11269:
11229:
11202:
11173:
10489:
10469:
10449:
10422:
10395:
10393:{\displaystyle s_{0}}
10368:
10339:
10207:
9908:
9881:
9843:
9810:
9777:
9747:
9675:
9645:
9616:
9017:
8931:
8901:
8835:
8782:
8736:
8716:
8714:{\displaystyle k_{b}}
8687:
8267:
8240:
8200:
8173:
8146:
8117:
7936:
7868:
7718:
7698:
7675:
7642:
7622:
7602:
7600:{\displaystyle k_{h}}
7575:
7546:
7456:
7429:
7238:
7214:
7190:
7166:
7142:
7122:
7120:{\displaystyle L_{d}}
7091:
7062:
6927:
6883:
6852:
6850:{\displaystyle k_{b}}
6825:
6823:{\displaystyle L_{d}}
6790:
6758:
6524:
6494:
6462:
6434:
6333:
6306:
6275:
6248:
6221:
6186:
6159:
6121:
6092:
5806:
5780:
5743:
5741:{\displaystyle T_{m}}
5716:
5714:{\displaystyle T_{0}}
5689:
5644:
5601:
5392:
5344:
5302:
5271:
5043:
4982:
4980:{\displaystyle J_{2}}
4951:
4927:
4880:
4851:
4822:
4796:
4569:
4547:
4527:
4525:{\displaystyle f_{0}}
4498:
4381:
4355:
4353:{\displaystyle \tau }
4335:
4298:
4272:
4246:
4209:
3861:
3847:
3477:
3464:
3319:
3065:
2930:
2928:{\displaystyle \eta }
2908:
2563:(by analogy with the
2561:Bingham–Maxwell model
2553:
2540:
2526:
2416:
2386:
2341:
2317:
2189:
2187:{\displaystyle N=1.0}
2161:
2081:
1936:
1841:
1819:
1720:
1718:{\displaystyle \eta }
1700:
1698:{\displaystyle \eta }
1678:
1561:
1528:
1492:
1476:
1447:
1401:
1332:
1193:
1060:
887:
870:
805:
740:
679:
672:Figure 3a. Creep test
671:
650:
616:
583:
507:Strain/Work hardening
487:
480:Strain hardening test
280:
249:
138:
114:
97:modulus of elasticity
90:
24:
12790:Plasticity (physics)
12021:, Stanford: Springer
11856:(in German): 582–592
11678:Plasticity (physics)
11648:is the atomic mass.
11632:
11628:is the density, and
11612:
11442:
11387:
11337:
11305:
11278:
11274:) are the values of
11238:
11211:
11184:
10503:
10478:
10458:
10431:
10404:
10377:
10350:
10220:
9928:
9890:
9852:
9819:
9786:
9756:
9684:
9654:
9627:
9030:
8945:
8913:
8844:
8791:
8745:
8725:
8698:
8285:
8249:
8209:
8182:
8155:
8128:
7955:
7879:
7729:
7707:
7687:
7651:
7631:
7611:
7584:
7557:
7467:
7438:
7261:
7227:
7203:
7188:{\displaystyle \nu }
7179:
7155:
7131:
7104:
7073:
6938:
6896:
6865:
6834:
6807:
6769:
6535:
6506:
6471:
6445:
6344:
6322:
6288:
6257:
6230:
6195:
6168:
6130:
6103:
5826:
5789:
5756:
5725:
5698:
5653:
5612:
5406:
5357:
5315:
5282:
5054:
5025:
4964:
4940:
4897:
4860:
4831:
4807:
4596:
4556:
4536:
4509:
4400:
4364:
4344:
4310:
4285:
4259:
4220:
3897:
3498:
3332:
3078:
2941:
2919:
2593:
2579:by analogy with the
2577:Bingham–Kelvin model
2573:Bingham–Norton model
2427:
2399:
2354:
2328:
2211:
2172:
2094:
1947:
1850:
1830:
1731:
1709:
1689:
1572:
1537:
1502:
1456:
1427:
1347:
1206:
1073:
899:
821:
756:
700:
625:
594:
533:
262:
151:
127:
103:
79:
12785:Continuum mechanics
12627:1994AIPC..309..989Z
12581:2003JAP....93..211P
12456:2000MMTA...31.1985G
12412:1996MMTA...27.2994C
12337:1987JAP....61.1816Z
12286:1977JMatS..12.1666H
12211:1980JAP....51.1498S
12115:Continuum Mechanics
12113:Irgens, F. (2008),
11982:1932JRheo...3...16H
11970:Journal of Rheology
11948:1930ZaMM...10..266R
11872:Betten, J. (2005),
11777:1990JMPSo..38..859B
11683:Continuum mechanics
11673:Creep (deformation)
11567:
11540:
11498:
11480:
11112:
11084:
11021:
10993:
10926:
10902:
10736:
10708:
10649:
10625:
10099:
10075:
9848:is a constant, and
9576:
9548:
9433:
9411:
9370:
9338:
9319:
9297:
7537:
7098:dislocation density
6801:dislocation segment
5804:{\displaystyle m=1}
5559:
5528:
5473:
5445:
4688:
4659:
4098:
4083:
4067:
4036:
4004:
3989:
3973:
3932:
3887:Perzyna formulation
3251:
3232:
3189:
3169:
3148:
3136:
3033:
3013:
2992:
2980:
2961:
2949:
2834:
2815:
2788:
2776:
2414:{\displaystyle K,m}
2049:
2015:
1994:
1982:
1765:
1753:
1662:
1650:
1374:
1355:
1311:
1292:
1245:
1214:
1172:
1153:
1109:
1081:
1033:
1002:
978:
950:
926:
907:
521:plastic yield limit
493:One consequence of
443:kinematic hardening
439:isotropic hardening
433:In 1960, the first
46:plastic deformation
34:continuum mechanics
12725:Scripta Materialia
12420:10.1007/BF02663849
12294:10.1007/BF00542818
12017:Hoff, ed. (1962),
11638:
11618:
11596:
11574:
11562:
11508:
11493:
11426:
11373:
11323:
11291:
11264:
11224:
11197:
11168:
11166:
11131:
11107:
11040:
11016:
10949:
10921:
10755:
10731:
10672:
10644:
10484:
10464:
10444:
10417:
10390:
10363:
10334:
10202:
10197:
10109:
10094:
9903:
9876:
9838:
9805:
9772:
9742:
9670:
9640:
9611:
9609:
9599:
9571:
9453:
9428:
9389:
9365:
9355:
9333:
9012:
8926:
8896:
8830:
8777:
8731:
8711:
8682:
8680:
8262:
8235:
8195:
8168:
8141:
8112:
7931:
7863:
7713:
7693:
7670:
7637:
7617:
7597:
7570:
7541:
7521:
7451:
7424:
7233:
7219:is the width of a
7209:
7185:
7161:
7137:
7117:
7086:
7057:
6922:
6878:
6859:Boltzmann constant
6847:
6820:
6785:
6753:
6519:
6489:
6457:
6429:
6328:
6301:
6270:
6243:
6216:
6181:
6154:
6116:
6087:
5801:
5775:
5738:
5711:
5684:
5639:
5596:
5592:
5554:
5499:
5468:
5387:
5339:
5297:
5266:
5038:
4977:
4946:
4922:
4889:Flow stress models
4875:
4846:
4817:
4791:
4786:
4695:
4683:
4564:
4542:
4522:
4493:
4376:
4350:
4330:
4293:
4267:
4241:
4204:
4199:
4110:
4093:
4074:
4062:
4016:
3999:
3980:
3968:
3864:
3842:
3840:
3480:
3459:
3314:
3266:
3246:
3196:
3184:
3155:
3143:
3060:
3040:
3028:
2999:
2987:
2968:
2956:
2925:
2903:
2901:
2849:
2829:
2795:
2783:
2556:
2543:
2521:
2411:
2381:
2336:
2312:
2184:
2156:
2076:
2056:
2044:
2001:
1989:
1931:
1836:
1814:
1794:
1760:
1715:
1695:
1673:
1669:
1657:
1556:
1523:
1495:
1471:
1442:
1396:
1386:
1369:
1327:
1323:
1306:
1257:
1240:
1188:
1184:
1167:
1121:
1104:
1055:
1045:
1028:
990:
973:
938:
921:
890:
865:
800:
735:
682:
674:
645:
611:
578:
491:
360:crash simulations,
275:
244:
133:
109:
85:
27:
12731:(12): 1125–1131,
12589:10.1063/1.1524706
12546:10.1115/1.1354990
12406:(10): 2994–3006,
12367:Acta Metallurgica
12141:978-0-02-372161-8
12131:Plasticity theory
12034:Plasticity Theory
11990:10.1122/1.2116434
11641:{\displaystyle M}
11576:
11566:
11539:
11510:
11497:
11479:
11468:
11454:
11349:
11133:
11127:
11111:
11104:
11083:
11042:
11036:
11020:
11013:
10992:
10951:
10946:
10925:
10917:
10901:
10884:
10757:
10751:
10735:
10728:
10707:
10674:
10669:
10648:
10640:
10624:
10607:
10487:{\displaystyle d}
10301:
10259:
10193:
10151:
10111:
10098:
10074:
9983:
9934:
9873:
9752:) are constants,
9601:
9596:
9575:
9568:
9547:
9527:
9455:
9432:
9410:
9391:
9369:
9357:
9337:
9318:
9296:
9244:
9242:
9207:
8988:
8951:
8906:) are constants.
8827:
8803:
8734:{\displaystyle b}
8624:
8622:
8612:
8585:
8537:
8429:
8427:
8417:
8390:
8342:
8110:
8001:
7961:
7854:
7788:
7640:{\displaystyle K}
7620:{\displaystyle l}
7513:
7512:
7420:
7395:
7316:
7267:
7236:{\displaystyle D}
7212:{\displaystyle w}
7164:{\displaystyle b}
7140:{\displaystyle a}
7055:
7009:
6710:
6667:
6631:
6626:
6583:
6556:
6331:{\displaystyle f}
6267:
6063:
6060:
6056:
6052:
6049:
6044:
6015:
5966:
5881:
5832:
5785:, we assume that
5694:non-dimensional.
5675:
5636:
5594:
5558:
5527:
5507:
5501:
5496:
5472:
5465:
5444:
5428:
5336:
5210:
5109:
5060:
4949:{\displaystyle f}
4713:
4697:
4687:
4658:
4609:
4545:{\displaystyle f}
4450:
4413:
4388:Macaulay brackets
4128:
4112:
4097:
4082:
4076:
4066:
4035:
4018:
4003:
3988:
3982:
3972:
3931:
3910:
3799:
3777:
3722:
3712:
3676:
3652:
3636:
3583:
3561:
3550:
3434:
3414:
3379:
3369:
3344:
3289:
3268:
3250:
3231:
3198:
3188:
3168:
3157:
3147:
3135:
3125:
3115:
3090:
3042:
3032:
3012:
3001:
2991:
2979:
2970:
2960:
2948:
2874:
2851:
2833:
2814:
2797:
2787:
2775:
2765:
2755:
2719:
2695:
2679:
2640:
2618:
2519:
2516:
2511:
2506:
2487:
2482:
2477:
2462:
2446:
2441:
2367:
2348:deviatoric stress
2298:
2287:
2254:
2242:
2230:
2124:
2108:
2058:
2048:
2014:
2003:
1993:
1981:
1960:
1929:
1896:
1839:{\displaystyle N}
1796:
1764:
1752:
1671:
1661:
1649:
1628:
1599:
1588:
1468:
1439:
1388:
1373:
1354:
1325:
1310:
1291:
1286:
1259:
1244:
1213:
1186:
1171:
1152:
1147:
1123:
1108:
1080:
1051:
1047:
1032:
1001:
992:
977:
949:
940:
925:
906:
519:The concept of a
420:deviatoric stress
294:overstress models
136:{\displaystyle N}
88:{\displaystyle E}
12797:
12770:
12769:
12761:(1–2): 181–187,
12746:
12740:
12739:
12716:
12710:
12709:
12682:
12676:
12675:
12659:(9): 2547–2555,
12644:
12638:
12637:
12610:
12604:
12598:
12592:
12591:
12558:
12549:
12548:
12527:
12521:
12520:
12503:
12501:cond-mat/0510330
12494:(3–4): 834–859,
12481:
12475:
12474:
12450:(8): 1985–1996,
12437:
12431:
12430:
12389:
12383:
12382:
12357:
12348:
12347:
12345:10.1063/1.338024
12314:
12305:
12304:
12280:(8): 1666–1672,
12267:
12258:
12257:
12256:
12255:
12233:
12222:
12221:
12219:10.1063/1.327799
12192:
12183:
12182:
12181:
12180:
12170:
12161:
12152:
12151:
12150:
12148:
12125:
12119:
12118:
12110:
12101:
12100:
12092:
12083:
12082:
12074:
12068:
12067:
12059:
12053:
12052:
12044:
12038:
12037:
12029:
12023:
12022:
12014:
12008:
12007:
11999:
11993:
11992:
11965:
11959:
11958:
11931:
11925:
11924:
11914:
11908:
11907:
11906:, Cambridge: 228
11899:
11893:
11892:
11884:
11878:
11877:
11869:
11858:
11857:
11849:
11843:
11842:
11834:
11828:
11827:
11815:
11809:
11808:
11794:
11788:
11787:
11758:
11752:
11751:
11744:
11731:
11730:
11722:
11716:
11715:
11703:
11647:
11645:
11644:
11639:
11627:
11625:
11624:
11619:
11605:
11603:
11602:
11597:
11595:
11594:
11590:
11581:
11577:
11575:
11573:
11563:
11561:
11536:
11529:
11528:
11524:
11515:
11511:
11509:
11507:
11494:
11492:
11476:
11469:
11461:
11456:
11455:
11447:
11435:
11433:
11432:
11427:
11425:
11424:
11412:
11411:
11399:
11398:
11382:
11380:
11379:
11374:
11372:
11371:
11362:
11351:
11350:
11342:
11332:
11330:
11329:
11324:
11300:
11298:
11297:
11292:
11290:
11289:
11273:
11271:
11270:
11265:
11263:
11262:
11250:
11249:
11233:
11231:
11230:
11225:
11223:
11222:
11207:is the value of
11206:
11204:
11203:
11198:
11196:
11195:
11177:
11175:
11174:
11169:
11167:
11163:
11159:
11158:
11157:
11156:
11152:
11151:
11150:
11149:
11148:
11138:
11134:
11132:
11130:
11129:
11128:
11120:
11108:
11106:
11105:
11100:
11099:
11098:
11088:
11080:
11073:
11072:
11060:
11059:
11058:
11057:
11047:
11043:
11041:
11039:
11038:
11037:
11029:
11017:
11015:
11014:
11009:
11008:
11007:
10997:
10989:
10982:
10981:
10961:
10957:
10956:
10952:
10950:
10948:
10947:
10942:
10941:
10940:
10930:
10922:
10920:
10919:
10918:
10910:
10898:
10886:
10885:
10877:
10866:
10850:
10849:
10837:
10836:
10821:
10820:
10796:
10795:
10782:
10778:
10777:
10776:
10775:
10774:
10773:
10772:
10762:
10758:
10756:
10754:
10753:
10752:
10744:
10732:
10730:
10729:
10724:
10723:
10722:
10712:
10704:
10697:
10696:
10684:
10680:
10679:
10675:
10673:
10671:
10670:
10665:
10664:
10663:
10653:
10645:
10643:
10642:
10641:
10633:
10621:
10609:
10608:
10600:
10589:
10573:
10572:
10560:
10559:
10544:
10543:
10519:
10518:
10493:
10491:
10490:
10485:
10473:
10471:
10470:
10465:
10453:
10451:
10450:
10445:
10443:
10442:
10426:
10424:
10423:
10418:
10416:
10415:
10400:is the value of
10399:
10397:
10396:
10391:
10389:
10388:
10372:
10370:
10369:
10364:
10362:
10361:
10343:
10341:
10340:
10335:
10302:
10297:
10296:
10295:
10283:
10282:
10272:
10260:
10255:
10254:
10253:
10241:
10240:
10230:
10211:
10209:
10208:
10203:
10201:
10200:
10194:
10191:
10169:
10168:
10152:
10149:
10127:
10123:
10122:
10118:
10117:
10113:
10112:
10110:
10108:
10095:
10093:
10092:
10091:
10090:
10071:
10023:
10022:
9985:
9984:
9979:
9978:
9977:
9967:
9961:
9960:
9959:
9946:
9945:
9935:
9932:
9912:
9910:
9909:
9904:
9902:
9901:
9885:
9883:
9882:
9877:
9875:
9874:
9869:
9868:
9867:
9857:
9847:
9845:
9844:
9839:
9837:
9836:
9814:
9812:
9811:
9806:
9804:
9803:
9781:
9779:
9778:
9773:
9771:
9770:
9751:
9749:
9748:
9743:
9735:
9734:
9722:
9721:
9709:
9708:
9696:
9695:
9679:
9677:
9676:
9671:
9669:
9668:
9649:
9647:
9646:
9641:
9639:
9638:
9620:
9618:
9617:
9612:
9610:
9606:
9602:
9600:
9598:
9597:
9592:
9591:
9590:
9580:
9572:
9570:
9569:
9564:
9563:
9562:
9552:
9544:
9532:
9528:
9526:
9507:
9506:
9497:
9496:
9480:
9472:
9456:
9454:
9452:
9451:
9450:
9429:
9427:
9426:
9425:
9407:
9392:
9390:
9388:
9366:
9364:
9363:
9359:
9358:
9356:
9354:
9353:
9352:
9334:
9332:
9331:
9330:
9315:
9293:
9281:
9280:
9258:
9257:
9245:
9243:
9238:
9237:
9236:
9226:
9224:
9222:
9221:
9209:
9208:
9203:
9202:
9201:
9191:
9182:
9181:
9169:
9168:
9152:
9151:
9135:
9134:
9119:
9118:
9097:
9096:
9072:
9071:
9052:
9051:
9021:
9019:
9018:
9013:
9008:
9007:
8989:
8987:
8986:
8985:
8984:
8970:
8969:
8968:
8955:
8952:
8949:
8935:
8933:
8932:
8927:
8925:
8924:
8905:
8903:
8902:
8897:
8895:
8894:
8882:
8881:
8869:
8868:
8856:
8855:
8839:
8837:
8836:
8831:
8829:
8828:
8823:
8822:
8821:
8811:
8805:
8804:
8796:
8786:
8784:
8783:
8778:
8776:
8775:
8760:
8759:
8740:
8738:
8737:
8732:
8720:
8718:
8717:
8712:
8710:
8709:
8691:
8689:
8688:
8683:
8681:
8677:
8676:
8675:
8674:
8665:
8656:
8652:
8651:
8650:
8649:
8648:
8639:
8630:
8626:
8625:
8623:
8615:
8613:
8608:
8607:
8606:
8596:
8594:
8586:
8584:
8565:
8564:
8555:
8554:
8541:
8535:
8534:
8533:
8523:
8496:
8495:
8482:
8481:
8480:
8479:
8470:
8461:
8457:
8456:
8455:
8454:
8453:
8444:
8435:
8431:
8430:
8428:
8420:
8418:
8413:
8412:
8411:
8401:
8399:
8391:
8389:
8370:
8369:
8360:
8359:
8346:
8340:
8339:
8338:
8328:
8301:
8300:
8271:
8269:
8268:
8263:
8261:
8260:
8244:
8242:
8241:
8236:
8234:
8233:
8221:
8220:
8204:
8202:
8201:
8196:
8194:
8193:
8177:
8175:
8174:
8169:
8167:
8166:
8150:
8148:
8147:
8142:
8140:
8139:
8121:
8119:
8118:
8113:
8111:
8109:
8108:
8099:
8079:
8074:
8073:
8064:
8063:
8051:
8050:
8041:
8040:
8025:
8024:
8003:
8002:
7994:
7988:
7987:
7986:
7973:
7972:
7962:
7959:
7940:
7938:
7937:
7932:
7930:
7929:
7917:
7916:
7904:
7903:
7891:
7890:
7872:
7870:
7869:
7864:
7856:
7855:
7850:
7849:
7848:
7838:
7826:
7825:
7813:
7812:
7790:
7789:
7784:
7783:
7782:
7772:
7760:
7759:
7747:
7746:
7722:
7720:
7719:
7714:
7702:
7700:
7699:
7694:
7679:
7677:
7676:
7671:
7669:
7668:
7646:
7644:
7643:
7638:
7626:
7624:
7623:
7618:
7606:
7604:
7603:
7598:
7596:
7595:
7579:
7577:
7576:
7571:
7569:
7568:
7550:
7548:
7547:
7542:
7536:
7531:
7530:
7514:
7508:
7507:
7506:
7497:
7492:
7491:
7479:
7478:
7460:
7458:
7457:
7452:
7450:
7449:
7433:
7431:
7430:
7425:
7418:
7396:
7394:
7393:
7392:
7382:
7380:
7379:
7340:
7339:
7318:
7317:
7312:
7311:
7310:
7300:
7294:
7293:
7292:
7279:
7278:
7268:
7265:
7245:drag coefficient
7242:
7240:
7239:
7234:
7218:
7216:
7215:
7210:
7194:
7192:
7191:
7186:
7170:
7168:
7167:
7162:
7146:
7144:
7143:
7138:
7126:
7124:
7123:
7118:
7116:
7115:
7095:
7093:
7092:
7087:
7085:
7084:
7066:
7064:
7063:
7058:
7056:
7054:
7053:
7052:
7043:
7042:
7029:
7024:
7023:
7010:
7008:
7007:
7006:
6993:
6989:
6988:
6976:
6975:
6966:
6965:
6955:
6950:
6949:
6931:
6929:
6928:
6923:
6921:
6920:
6908:
6907:
6892:. The constants
6887:
6885:
6884:
6879:
6877:
6876:
6856:
6854:
6853:
6848:
6846:
6845:
6829:
6827:
6826:
6821:
6819:
6818:
6794:
6792:
6791:
6786:
6784:
6783:
6762:
6760:
6759:
6754:
6752:
6751:
6739:
6738:
6725:
6724:
6716:
6712:
6711:
6709:
6708:
6699:
6698:
6689:
6684:
6680:
6679:
6678:
6673:
6669:
6668:
6666:
6665:
6656:
6655:
6646:
6632:
6630:
6624:
6623:
6622:
6612:
6611:
6610:
6597:
6584:
6582:
6581:
6569:
6558:
6557:
6552:
6551:
6550:
6540:
6528:
6526:
6525:
6520:
6518:
6517:
6498:
6496:
6495:
6490:
6485:
6484:
6483:
6466:
6464:
6463:
6458:
6438:
6436:
6435:
6430:
6428:
6427:
6412:
6411:
6410:
6397:
6396:
6395:
6364:
6363:
6362:
6337:
6335:
6334:
6329:
6310:
6308:
6307:
6302:
6300:
6299:
6279:
6277:
6276:
6271:
6269:
6268:
6265:
6252:
6250:
6249:
6244:
6242:
6241:
6225:
6223:
6222:
6217:
6190:
6188:
6187:
6182:
6180:
6179:
6163:
6161:
6160:
6155:
6150:
6149:
6148:
6125:
6123:
6122:
6117:
6115:
6114:
6096:
6094:
6093:
6088:
6086:
6085:
6073:
6072:
6061:
6058:
6057:
6054:
6050:
6047:
6046:
6045:
6042:
6030:
6029:
6016:
6014:
6013:
6004:
5984:
5982:
5978:
5968:
5967:
5962:
5961:
5960:
5950:
5944:
5943:
5928:
5927:
5926:
5910:
5909:
5883:
5882:
5877:
5876:
5875:
5865:
5859:
5858:
5857:
5844:
5843:
5833:
5830:
5810:
5808:
5807:
5802:
5784:
5782:
5781:
5776:
5768:
5767:
5750:melt temperature
5747:
5745:
5744:
5739:
5737:
5736:
5720:
5718:
5717:
5712:
5710:
5709:
5693:
5691:
5690:
5685:
5683:
5682:
5677:
5676:
5671:
5670:
5669:
5659:
5648:
5646:
5645:
5640:
5638:
5637:
5632:
5631:
5630:
5617:
5605:
5603:
5602:
5597:
5595:
5593:
5591:
5587:
5586:
5574:
5573:
5555:
5553:
5549:
5548:
5524:
5519:
5518:
5508:
5505:
5502:
5500:
5498:
5497:
5492:
5491:
5490:
5477:
5469:
5467:
5466:
5461:
5460:
5459:
5449:
5441:
5436:
5435:
5430:
5429:
5424:
5423:
5422:
5412:
5396:
5394:
5393:
5388:
5349:is the plastic
5348:
5346:
5345:
5340:
5338:
5337:
5332:
5331:
5330:
5320:
5306:
5304:
5303:
5298:
5296:
5295:
5294:
5275:
5273:
5272:
5267:
5265:
5261:
5260:
5259:
5250:
5249:
5226:
5222:
5218:
5217:
5212:
5211:
5206:
5205:
5204:
5194:
5167:
5163:
5162:
5161:
5152:
5151:
5150:
5111:
5110:
5105:
5104:
5103:
5093:
5087:
5086:
5085:
5072:
5071:
5061:
5058:
5047:
5045:
5044:
5039:
5037:
5036:
4986:
4984:
4983:
4978:
4976:
4975:
4955:
4953:
4952:
4947:
4931:
4929:
4928:
4923:
4918:
4910:
4884:
4882:
4881:
4876:
4874:
4869:
4868:
4855:
4853:
4852:
4847:
4845:
4840:
4839:
4826:
4824:
4823:
4818:
4816:
4815:
4800:
4798:
4797:
4792:
4790:
4789:
4783:
4782:
4743:
4742:
4732:
4724:
4711:
4710:
4698:
4696:
4694:
4684:
4682:
4681:
4676:
4675:
4666:
4655:
4650:
4649:
4641:
4640:
4622:
4621:
4620:
4611:
4610:
4602:
4573:
4571:
4570:
4565:
4563:
4551:
4549:
4548:
4543:
4531:
4529:
4528:
4523:
4521:
4520:
4502:
4500:
4499:
4494:
4489:
4481:
4461:
4460:
4455:
4451:
4449:
4448:
4436:
4426:
4425:
4424:
4415:
4414:
4406:
4385:
4383:
4382:
4377:
4359:
4357:
4356:
4351:
4339:
4337:
4336:
4331:
4329:
4328:
4327:
4318:
4302:
4300:
4299:
4294:
4292:
4276:
4274:
4273:
4268:
4266:
4250:
4248:
4247:
4242:
4213:
4211:
4210:
4205:
4203:
4202:
4196:
4195:
4147:
4139:
4126:
4125:
4124:
4113:
4111:
4109:
4108:
4094:
4092:
4079:
4077:
4075:
4073:
4063:
4061:
4057:
4049:
4032:
4019:
4017:
4015:
4014:
4000:
3998:
3985:
3983:
3981:
3979:
3969:
3967:
3966:
3962:
3958:
3950:
3928:
3923:
3922:
3921:
3912:
3911:
3903:
3851:
3849:
3848:
3843:
3841:
3837:
3836:
3824:
3819:
3814:
3809:
3804:
3797:
3796:
3784:
3782:
3775:
3771:
3770:
3769:
3760:
3751:
3750:
3738:
3724:
3723:
3715:
3710:
3709:
3708:
3700:
3699:
3689:
3688:
3687:
3678:
3677:
3669:
3662:
3661:
3660:
3654:
3653:
3645:
3638:
3637:
3629:
3625:
3621:
3620:
3608:
3603:
3598:
3593:
3588:
3581:
3580:
3568:
3566:
3559:
3555:
3548:
3547:
3546:
3538:
3537:
3527:
3526:
3525:
3519:
3510:
3504:
3489:strain hardening
3468:
3466:
3465:
3460:
3458:
3457:
3442:
3432:
3431:
3419:
3412:
3408:
3407:
3395:
3381:
3380:
3372:
3367:
3366:
3365:
3357:
3356:
3346:
3345:
3337:
3323:
3321:
3320:
3315:
3313:
3312:
3297:
3287:
3286:
3274:
3270:
3269:
3267:
3265:
3261:
3247:
3245:
3244:
3243:
3228:
3215:
3214:
3203:
3199:
3197:
3195:
3185:
3183:
3179:
3165:
3158:
3156:
3154:
3144:
3142:
3132:
3127:
3126:
3118:
3113:
3112:
3111:
3103:
3102:
3092:
3091:
3083:
3069:
3067:
3066:
3061:
3059:
3058:
3047:
3043:
3041:
3039:
3029:
3027:
3023:
3009:
3002:
3000:
2998:
2988:
2986:
2976:
2971:
2969:
2967:
2957:
2955:
2945:
2934:
2932:
2931:
2926:
2912:
2910:
2909:
2904:
2902:
2898:
2897:
2882:
2872:
2871:
2859:
2857:
2853:
2852:
2850:
2848:
2844:
2830:
2828:
2827:
2826:
2811:
2798:
2796:
2794:
2784:
2782:
2772:
2767:
2766:
2758:
2753:
2752:
2751:
2743:
2742:
2732:
2731:
2730:
2721:
2720:
2712:
2705:
2704:
2703:
2697:
2696:
2688:
2681:
2680:
2672:
2668:
2664:
2663:
2648:
2638:
2637:
2625:
2623:
2616:
2615:
2614:
2605:
2599:
2530:
2528:
2527:
2522:
2520:
2518:
2517:
2512:
2507:
2499:
2497:
2495:
2489:
2488:
2483:
2478:
2470:
2468:
2466:
2463:
2455:
2453:
2448:
2447:
2442:
2434:
2432:
2420:
2418:
2417:
2412:
2390:
2388:
2387:
2382:
2380:
2379:
2378:
2369:
2368:
2360:
2345:
2343:
2342:
2337:
2335:
2321:
2319:
2318:
2313:
2311:
2310:
2309:
2300:
2299:
2291:
2285:
2284:
2283:
2272:
2268:
2267:
2266:
2265:
2256:
2255:
2247:
2243:
2238:
2228:
2218:
2193:
2191:
2190:
2185:
2165:
2163:
2162:
2157:
2155:
2154:
2150:
2141:
2137:
2136:
2135:
2126:
2125:
2117:
2106:
2085:
2083:
2082:
2077:
2075:
2074:
2063:
2059:
2057:
2055:
2045:
2043:
2042:
2037:
2032:
2027:
2022:
2011:
2004:
2002:
2000:
1990:
1988:
1978:
1973:
1972:
1971:
1962:
1961:
1953:
1940:
1938:
1937:
1932:
1930:
1928:
1927:
1915:
1914:
1902:
1897:
1895:
1887:
1882:
1877:
1872:
1867:
1862:
1857:
1845:
1843:
1842:
1837:
1823:
1821:
1820:
1815:
1813:
1812:
1801:
1797:
1795:
1793:
1792:
1787:
1782:
1777:
1772:
1761:
1759:
1749:
1724:
1722:
1721:
1716:
1704:
1702:
1701:
1696:
1682:
1680:
1679:
1674:
1672:
1670:
1668:
1658:
1656:
1646:
1641:
1640:
1639:
1630:
1629:
1621:
1612:
1611:
1610:
1601:
1600:
1592:
1586:
1579:
1565:
1563:
1562:
1557:
1549:
1548:
1532:
1530:
1529:
1524:
1516:
1515:
1510:
1481:, respectively.
1480:
1478:
1477:
1472:
1470:
1469:
1461:
1451:
1449:
1448:
1443:
1441:
1440:
1432:
1405:
1403:
1402:
1397:
1389:
1387:
1385:
1381:
1370:
1368:
1367:
1362:
1351:
1336:
1334:
1333:
1328:
1326:
1324:
1322:
1318:
1307:
1305:
1304:
1299:
1288:
1284:
1283:
1282:
1274:
1273:
1260:
1258:
1256:
1252:
1241:
1239:
1238:
1237:
1236:
1227:
1221:
1210:
1197:
1195:
1194:
1189:
1187:
1185:
1183:
1179:
1168:
1166:
1165:
1160:
1149:
1145:
1144:
1143:
1135:
1134:
1124:
1122:
1120:
1116:
1105:
1103:
1102:
1101:
1100:
1094:
1088:
1077:
1064:
1062:
1061:
1056:
1049:
1048:
1046:
1044:
1040:
1029:
1027:
1026:
1025:
1024:
1015:
1009:
998:
993:
991:
989:
985:
974:
972:
971:
970:
969:
963:
957:
946:
941:
939:
937:
933:
922:
920:
919:
914:
903:
874:
872:
871:
866:
861:
860:
855:
846:
838:
837:
832:
809:
807:
806:
801:
796:
795:
790:
781:
773:
772:
767:
744:
742:
741:
736:
731:
730:
725:
716:
654:
652:
651:
646:
644:
643:
642:
633:
620:
618:
617:
612:
610:
609:
608:
602:
587:
585:
584:
579:
577:
576:
575:
566:
557:
556:
555:
549:
540:
455:phenomenological
284:
282:
281:
276:
274:
273:
253:
251:
250:
247:{\displaystyle }
245:
240:
239:
235:
219:
214:
206:
180:
175:
167:
142:
140:
139:
134:
118:
116:
115:
110:
94:
92:
91:
86:
12805:
12804:
12800:
12799:
12798:
12796:
12795:
12794:
12775:
12774:
12773:
12747:
12743:
12717:
12713:
12683:
12679:
12645:
12641:
12635:10.1063/1.46201
12611:
12607:
12599:
12595:
12559:
12552:
12528:
12524:
12482:
12478:
12438:
12434:
12390:
12386:
12358:
12351:
12315:
12308:
12268:
12261:
12253:
12251:
12234:
12225:
12193:
12186:
12178:
12176:
12168:
12162:
12155:
12146:
12144:
12142:
12126:
12122:
12111:
12104:
12093:
12086:
12075:
12071:
12060:
12056:
12045:
12041:
12030:
12026:
12015:
12011:
12000:
11996:
11966:
11962:
11932:
11928:
11915:
11911:
11900:
11896:
11885:
11881:
11874:Creep Mechanics
11870:
11861:
11850:
11846:
11835:
11831:
11816:
11812:
11795:
11791:
11759:
11755:
11745:
11734:
11723:
11719:
11704:
11700:
11696:
11663:Bingham plastic
11658:Viscoelasticity
11654:
11633:
11630:
11629:
11613:
11610:
11609:
11586:
11582:
11569:
11564:
11542:
11537:
11535:
11531:
11530:
11520:
11516:
11500:
11495:
11482:
11477:
11475:
11471:
11470:
11460:
11446:
11445:
11443:
11440:
11439:
11420:
11416:
11407:
11403:
11394:
11390:
11388:
11385:
11384:
11367:
11363:
11358:
11341:
11340:
11338:
11335:
11334:
11306:
11303:
11302:
11285:
11281:
11279:
11276:
11275:
11258:
11254:
11245:
11241:
11239:
11236:
11235:
11218:
11214:
11212:
11209:
11208:
11191:
11187:
11185:
11182:
11181:
11165:
11164:
11144:
11140:
11139:
11119:
11118:
11114:
11109:
11094:
11093:
11089:
11087:
11086:
11081:
11079:
11075:
11074:
11068:
11064:
11053:
11049:
11048:
11028:
11027:
11023:
11018:
11003:
11002:
10998:
10996:
10995:
10990:
10988:
10984:
10983:
10977:
10973:
10972:
10968:
10936:
10935:
10931:
10929:
10928:
10923:
10909:
10908:
10904:
10899:
10897:
10893:
10876:
10875:
10871:
10867:
10856:
10855:
10854:
10845:
10841:
10832:
10828:
10816:
10812:
10811:
10807:
10797:
10791:
10787:
10784:
10783:
10768:
10764:
10763:
10743:
10742:
10738:
10733:
10718:
10717:
10713:
10711:
10710:
10705:
10703:
10699:
10698:
10692:
10688:
10659:
10658:
10654:
10652:
10651:
10646:
10632:
10631:
10627:
10622:
10620:
10616:
10599:
10598:
10594:
10590:
10579:
10578:
10577:
10568:
10564:
10555:
10551:
10539:
10535:
10534:
10530:
10520:
10514:
10510:
10506:
10504:
10501:
10500:
10479:
10476:
10475:
10459:
10456:
10455:
10438:
10434:
10432:
10429:
10428:
10411:
10407:
10405:
10402:
10401:
10384:
10380:
10378:
10375:
10374:
10357:
10353:
10351:
10348:
10347:
10291:
10287:
10278:
10274:
10273:
10271:
10249:
10245:
10236:
10232:
10231:
10229:
10221:
10218:
10217:
10196:
10195:
10190:
10188:
10164:
10160:
10154:
10153:
10148:
10146:
10101:
10096:
10086:
10085:
10081:
10077:
10072:
10070:
10060:
10056:
10040:
10036:
10018:
10014:
10013:
10009:
9999:
9998:
9973:
9972:
9968:
9966:
9965:
9955:
9954:
9950:
9941:
9937:
9931:
9929:
9926:
9925:
9919:
9897:
9893:
9891:
9888:
9887:
9863:
9862:
9858:
9856:
9855:
9853:
9850:
9849:
9826:
9822:
9820:
9817:
9816:
9793:
9789:
9787:
9784:
9783:
9763:
9759:
9757:
9754:
9753:
9730:
9726:
9717:
9713:
9704:
9700:
9691:
9687:
9685:
9682:
9681:
9661:
9657:
9655:
9652:
9651:
9634:
9630:
9628:
9625:
9624:
9608:
9607:
9586:
9585:
9581:
9579:
9578:
9573:
9558:
9557:
9553:
9551:
9550:
9545:
9543:
9539:
9502:
9498:
9486:
9482:
9481:
9473:
9471:
9467:
9460:
9440:
9436:
9435:
9430:
9418:
9414:
9413:
9408:
9406:
9394:
9393:
9372:
9367:
9345:
9341:
9340:
9335:
9326:
9322:
9321:
9316:
9314:
9310:
9306:
9299:
9294:
9292:
9285:
9276:
9272:
9263:
9262:
9253:
9249:
9232:
9231:
9227:
9225:
9223:
9217:
9213:
9197:
9196:
9192:
9190:
9189:
9177:
9173:
9164:
9160:
9153:
9147:
9143:
9140:
9139:
9130:
9126:
9111:
9107:
9092:
9088:
9067:
9063:
9056:
9047:
9043:
9033:
9031:
9028:
9027:
9003:
8999:
8980:
8979:
8975:
8971:
8964:
8960:
8956:
8954:
8948:
8946:
8943:
8942:
8920:
8916:
8914:
8911:
8910:
8890:
8886:
8877:
8873:
8864:
8860:
8851:
8847:
8845:
8842:
8841:
8817:
8816:
8812:
8810:
8809:
8795:
8794:
8792:
8789:
8788:
8768:
8764:
8752:
8748:
8746:
8743:
8742:
8726:
8723:
8722:
8705:
8701:
8699:
8696:
8695:
8679:
8678:
8670:
8666:
8661:
8657:
8644:
8640:
8635:
8631:
8614:
8602:
8601:
8597:
8595:
8593:
8560:
8556:
8547:
8543:
8542:
8529:
8525:
8524:
8522:
8521:
8517:
8516:
8509:
8505:
8504:
8497:
8491:
8487:
8484:
8483:
8475:
8471:
8466:
8462:
8449:
8445:
8440:
8436:
8419:
8407:
8406:
8402:
8400:
8398:
8365:
8361:
8352:
8348:
8347:
8334:
8330:
8329:
8327:
8326:
8322:
8321:
8314:
8310:
8309:
8302:
8296:
8292:
8288:
8286:
8283:
8282:
8256:
8252:
8250:
8247:
8246:
8229:
8225:
8216:
8212:
8210:
8207:
8206:
8189:
8185:
8183:
8180:
8179:
8162:
8158:
8156:
8153:
8152:
8135:
8131:
8129:
8126:
8125:
8104:
8100:
8080:
8078:
8069:
8065:
8059:
8055:
8046:
8042:
8036:
8032:
8020:
8016:
7993:
7992:
7982:
7981:
7977:
7968:
7964:
7958:
7956:
7953:
7952:
7947:
7925:
7921:
7912:
7908:
7899:
7895:
7886:
7882:
7880:
7877:
7876:
7844:
7843:
7839:
7837:
7836:
7821:
7817:
7808:
7804:
7778:
7777:
7773:
7771:
7770:
7755:
7751:
7742:
7738:
7730:
7727:
7726:
7708:
7705:
7704:
7688:
7685:
7684:
7664:
7660:
7652:
7649:
7648:
7632:
7629:
7628:
7612:
7609:
7608:
7591:
7587:
7585:
7582:
7581:
7564:
7560:
7558:
7555:
7554:
7532:
7526:
7525:
7502:
7498:
7496:
7487:
7483:
7474:
7470:
7468:
7465:
7464:
7445:
7441:
7439:
7436:
7435:
7434:In this model,
7388:
7387:
7383:
7381:
7375:
7371:
7335:
7331:
7306:
7305:
7301:
7299:
7298:
7288:
7287:
7283:
7274:
7270:
7264:
7262:
7259:
7258:
7253:
7228:
7225:
7224:
7204:
7201:
7200:
7197:Debye frequency
7180:
7177:
7176:
7156:
7153:
7152:
7149:Peierls valleys
7132:
7129:
7128:
7111:
7107:
7105:
7102:
7101:
7080:
7076:
7074:
7071:
7070:
7048:
7044:
7038:
7034:
7033:
7028:
7019:
7015:
7002:
6998:
6994:
6984:
6980:
6971:
6967:
6961:
6957:
6956:
6954:
6945:
6941:
6939:
6936:
6935:
6916:
6912:
6903:
6899:
6897:
6894:
6893:
6872:
6868:
6866:
6863:
6862:
6841:
6837:
6835:
6832:
6831:
6814:
6810:
6808:
6805:
6804:
6779:
6775:
6770:
6767:
6766:
6747:
6743:
6734:
6730:
6717:
6704:
6700:
6694:
6690:
6688:
6674:
6661:
6657:
6651:
6647:
6645:
6638:
6634:
6633:
6618:
6614:
6613:
6606:
6602:
6598:
6596:
6595:
6591:
6577:
6573:
6568:
6567:
6563:
6562:
6546:
6545:
6541:
6539:
6538:
6536:
6533:
6532:
6513:
6509:
6507:
6504:
6503:
6479:
6478:
6474:
6472:
6469:
6468:
6446:
6443:
6442:
6423:
6419:
6406:
6405:
6401:
6391:
6390:
6386:
6358:
6357:
6353:
6345:
6342:
6341:
6338:) has the form
6323:
6320:
6319:
6295:
6291:
6289:
6286:
6285:
6264:
6260:
6258:
6255:
6254:
6237:
6233:
6231:
6228:
6227:
6196:
6193:
6192:
6175:
6171:
6169:
6166:
6165:
6144:
6143:
6139:
6131:
6128:
6127:
6110:
6106:
6104:
6101:
6100:
6081:
6077:
6068:
6064:
6053:
6041:
6037:
6025:
6021:
6009:
6005:
5985:
5983:
5956:
5955:
5951:
5949:
5948:
5939:
5935:
5922:
5921:
5917:
5905:
5901:
5900:
5896:
5871:
5870:
5866:
5864:
5863:
5853:
5852:
5848:
5839:
5835:
5829:
5827:
5824:
5823:
5817:
5790:
5787:
5786:
5763:
5759:
5757:
5754:
5753:
5748:is a reference
5732:
5728:
5726:
5723:
5722:
5705:
5701:
5699:
5696:
5695:
5678:
5665:
5664:
5660:
5658:
5657:
5656:
5654:
5651:
5650:
5623:
5622:
5618:
5616:
5615:
5613:
5610:
5609:
5582:
5578:
5569:
5565:
5561:
5556:
5544:
5540:
5530:
5525:
5523:
5514:
5510:
5504:
5483:
5482:
5478:
5476:
5475:
5470:
5455:
5454:
5450:
5448:
5447:
5442:
5440:
5431:
5418:
5417:
5413:
5411:
5410:
5409:
5407:
5404:
5403:
5358:
5355:
5354:
5326:
5325:
5321:
5319:
5318:
5316:
5313:
5312:
5290:
5289:
5285:
5283:
5280:
5279:
5255:
5251:
5245:
5241:
5231:
5227:
5213:
5200:
5199:
5195:
5193:
5192:
5191:
5172:
5168:
5157:
5153:
5146:
5145:
5141:
5128:
5124:
5099:
5098:
5094:
5092:
5091:
5081:
5080:
5076:
5067:
5063:
5057:
5055:
5052:
5051:
5032:
5028:
5026:
5023:
5022:
5019:
4971:
4967:
4965:
4962:
4961:
4941:
4938:
4937:
4914:
4906:
4898:
4895:
4894:
4891:
4870:
4864:
4863:
4861:
4858:
4857:
4841:
4835:
4834:
4832:
4829:
4828:
4811:
4810:
4808:
4805:
4804:
4785:
4784:
4754:
4753:
4751:
4745:
4744:
4728:
4720:
4703:
4702:
4701:
4699:
4690:
4685:
4677:
4671:
4670:
4662:
4661:
4656:
4654:
4642:
4636:
4635:
4634:
4627:
4626:
4613:
4612:
4601:
4600:
4599:
4597:
4594:
4593:
4588:
4559:
4557:
4554:
4553:
4537:
4534:
4533:
4516:
4512:
4510:
4507:
4506:
4485:
4477:
4456:
4444:
4440:
4435:
4431:
4430:
4417:
4416:
4405:
4404:
4403:
4401:
4398:
4397:
4365:
4362:
4361:
4345:
4342:
4341:
4320:
4319:
4314:
4313:
4311:
4308:
4307:
4288:
4286:
4283:
4282:
4262:
4260:
4257:
4256:
4221:
4218:
4217:
4198:
4197:
4167:
4166:
4164:
4158:
4157:
4143:
4135:
4117:
4116:
4114:
4104:
4100:
4095:
4085:
4080:
4078:
4069:
4064:
4053:
4045:
4038:
4033:
4031:
4024:
4023:
4010:
4006:
4001:
3991:
3986:
3984:
3975:
3970:
3954:
3946:
3939:
3935:
3934:
3929:
3927:
3914:
3913:
3902:
3901:
3900:
3898:
3895:
3894:
3889:
3869:
3839:
3838:
3832:
3828:
3820:
3815:
3810:
3805:
3800:
3786:
3783:
3778:
3762:
3761:
3756:
3755:
3746:
3742:
3734:
3714:
3713:
3701:
3695:
3694:
3693:
3680:
3679:
3668:
3667:
3666:
3656:
3655:
3644:
3643:
3642:
3628:
3627:
3623:
3622:
3616:
3612:
3604:
3599:
3594:
3589:
3584:
3570:
3567:
3562:
3551:
3539:
3533:
3532:
3531:
3521:
3520:
3515:
3514:
3506:
3501:
3499:
3496:
3495:
3485:
3453:
3449:
3438:
3421:
3415:
3403:
3399:
3391:
3371:
3370:
3358:
3352:
3351:
3350:
3336:
3335:
3333:
3330:
3329:
3308:
3304:
3293:
3276:
3257:
3253:
3248:
3239:
3235:
3234:
3229:
3227:
3220:
3216:
3204:
3191:
3186:
3175:
3171:
3166:
3164:
3160:
3159:
3150:
3145:
3138:
3133:
3131:
3117:
3116:
3104:
3098:
3097:
3096:
3082:
3081:
3079:
3076:
3075:
3048:
3035:
3030:
3019:
3015:
3010:
3008:
3004:
3003:
2994:
2989:
2982:
2977:
2975:
2963:
2958:
2951:
2946:
2944:
2942:
2939:
2938:
2920:
2917:
2916:
2900:
2899:
2893:
2889:
2878:
2861:
2858:
2840:
2836:
2831:
2822:
2818:
2817:
2812:
2810:
2803:
2799:
2790:
2785:
2778:
2773:
2771:
2757:
2756:
2744:
2738:
2737:
2736:
2723:
2722:
2711:
2710:
2709:
2699:
2698:
2687:
2686:
2685:
2671:
2670:
2666:
2665:
2659:
2655:
2644:
2627:
2624:
2619:
2610:
2609:
2601:
2596:
2594:
2591:
2590:
2548:
2498:
2496:
2494:
2493:
2469:
2467:
2465:
2464:
2454:
2452:
2433:
2431:
2430:
2428:
2425:
2424:
2400:
2397:
2396:
2371:
2370:
2359:
2358:
2357:
2355:
2352:
2351:
2331:
2329:
2326:
2325:
2302:
2301:
2290:
2289:
2288:
2273:
2258:
2257:
2246:
2245:
2244:
2237:
2236:
2232:
2231:
2214:
2212:
2209:
2208:
2173:
2170:
2169:
2146:
2142:
2128:
2127:
2116:
2115:
2114:
2110:
2109:
2095:
2092:
2091:
2064:
2051:
2046:
2038:
2033:
2028:
2023:
2018:
2017:
2012:
2010:
2006:
2005:
1996:
1991:
1984:
1979:
1977:
1964:
1963:
1952:
1951:
1950:
1948:
1945:
1944:
1920:
1916:
1907:
1903:
1901:
1891:
1883:
1881:
1873:
1868:
1863:
1858:
1853:
1851:
1848:
1847:
1831:
1828:
1827:
1802:
1788:
1783:
1778:
1773:
1768:
1767:
1762:
1755:
1750:
1748:
1744:
1743:
1732:
1729:
1728:
1710:
1707:
1706:
1690:
1687:
1686:
1664:
1659:
1652:
1647:
1645:
1632:
1631:
1620:
1619:
1618:
1603:
1602:
1591:
1590:
1589:
1575:
1573:
1570:
1569:
1544:
1540:
1538:
1535:
1534:
1511:
1506:
1505:
1503:
1500:
1499:
1487:
1460:
1459:
1457:
1454:
1453:
1431:
1430:
1428:
1425:
1424:
1412:
1377:
1376:
1371:
1363:
1358:
1357:
1352:
1350:
1348:
1345:
1344:
1314:
1313:
1308:
1300:
1295:
1294:
1289:
1287:
1275:
1269:
1268:
1267:
1248:
1247:
1242:
1229:
1228:
1223:
1222:
1217:
1216:
1211:
1209:
1207:
1204:
1203:
1175:
1174:
1169:
1161:
1156:
1155:
1150:
1148:
1136:
1130:
1129:
1128:
1112:
1111:
1106:
1096:
1095:
1090:
1089:
1084:
1083:
1078:
1076:
1074:
1071:
1070:
1036:
1035:
1030:
1017:
1016:
1011:
1010:
1005:
1004:
999:
997:
981:
980:
975:
965:
964:
959:
958:
953:
952:
947:
945:
929:
928:
923:
915:
910:
909:
904:
902:
900:
897:
896:
882:
880:Relaxation test
856:
851:
850:
842:
833:
828:
827:
822:
819:
818:
791:
786:
785:
777:
768:
763:
762:
757:
754:
753:
750:secondary creep
726:
721:
720:
712:
701:
698:
697:
666:
635:
634:
629:
628:
626:
623:
622:
604:
603:
598:
597:
595:
592:
591:
568:
567:
562:
561:
551:
550:
545:
544:
536:
534:
531:
530:
482:
463:
405:secondary creep
373:
342:viscoelasticity
269:
265:
263:
260:
259:
231:
227:
223:
215:
210:
202:
176:
171:
163:
152:
149:
148:
128:
125:
124:
104:
101:
100:
80:
77:
76:
69:viscoelasticity
32:is a theory in
30:Viscoplasticity
17:
12:
11:
5:
12803:
12793:
12792:
12787:
12772:
12771:
12741:
12711:
12687:Acta Mechanica
12677:
12639:
12621:(1): 989–992,
12605:
12593:
12575:(1): 211–220,
12550:
12522:
12476:
12432:
12384:
12349:
12306:
12259:
12223:
12184:
12153:
12140:
12120:
12102:
12084:
12069:
12054:
12039:
12024:
12009:
11994:
11960:
11942:(3): 266–274,
11926:
11909:
11894:
11879:
11859:
11844:
11829:
11810:
11789:
11771:(6): 859–874,
11753:
11732:
11717:
11697:
11695:
11692:
11691:
11690:
11685:
11680:
11675:
11670:
11665:
11660:
11653:
11650:
11637:
11617:
11593:
11589:
11585:
11580:
11572:
11560:
11557:
11554:
11551:
11548:
11545:
11534:
11527:
11523:
11519:
11514:
11506:
11503:
11491:
11488:
11485:
11474:
11467:
11464:
11459:
11453:
11450:
11423:
11419:
11415:
11410:
11406:
11402:
11397:
11393:
11370:
11366:
11361:
11357:
11354:
11348:
11345:
11322:
11319:
11316:
11313:
11310:
11288:
11284:
11261:
11257:
11253:
11248:
11244:
11221:
11217:
11194:
11190:
11162:
11155:
11147:
11143:
11137:
11126:
11123:
11117:
11103:
11097:
11092:
11078:
11071:
11067:
11063:
11056:
11052:
11046:
11035:
11032:
11026:
11012:
11006:
11001:
10987:
10980:
10976:
10971:
10967:
10964:
10960:
10955:
10945:
10939:
10934:
10916:
10913:
10907:
10896:
10892:
10889:
10883:
10880:
10874:
10870:
10865:
10862:
10859:
10853:
10848:
10844:
10840:
10835:
10831:
10827:
10824:
10819:
10815:
10810:
10806:
10803:
10800:
10798:
10794:
10790:
10786:
10785:
10781:
10771:
10767:
10761:
10750:
10747:
10741:
10727:
10721:
10716:
10702:
10695:
10691:
10687:
10683:
10678:
10668:
10662:
10657:
10639:
10636:
10630:
10619:
10615:
10612:
10606:
10603:
10597:
10593:
10588:
10585:
10582:
10576:
10571:
10567:
10563:
10558:
10554:
10550:
10547:
10542:
10538:
10533:
10529:
10526:
10523:
10521:
10517:
10513:
10509:
10508:
10483:
10463:
10441:
10437:
10414:
10410:
10387:
10383:
10360:
10356:
10333:
10330:
10327:
10324:
10321:
10318:
10315:
10312:
10309:
10305:
10300:
10294:
10290:
10286:
10281:
10277:
10270:
10267:
10263:
10258:
10252:
10248:
10244:
10239:
10235:
10228:
10225:
10199:
10189:
10187:
10184:
10181:
10178:
10175:
10172:
10167:
10163:
10159:
10156:
10155:
10150:thermal regime
10147:
10145:
10142:
10139:
10136:
10133:
10130:
10126:
10121:
10116:
10107:
10104:
10089:
10084:
10080:
10069:
10066:
10063:
10059:
10055:
10052:
10049:
10046:
10043:
10039:
10035:
10032:
10029:
10026:
10021:
10017:
10012:
10008:
10005:
10004:
10002:
9997:
9994:
9991:
9988:
9982:
9976:
9971:
9964:
9958:
9953:
9949:
9944:
9940:
9918:
9915:
9900:
9896:
9872:
9866:
9861:
9835:
9832:
9829:
9825:
9802:
9799:
9796:
9792:
9769:
9766:
9762:
9741:
9738:
9733:
9729:
9725:
9720:
9716:
9712:
9707:
9703:
9699:
9694:
9690:
9667:
9664:
9660:
9637:
9633:
9605:
9595:
9589:
9584:
9567:
9561:
9556:
9542:
9538:
9535:
9531:
9525:
9522:
9519:
9516:
9513:
9510:
9505:
9501:
9495:
9492:
9489:
9485:
9479:
9476:
9470:
9466:
9463:
9461:
9459:
9449:
9446:
9443:
9439:
9424:
9421:
9417:
9405:
9402:
9399:
9396:
9395:
9387:
9384:
9381:
9378:
9375:
9362:
9351:
9348:
9344:
9329:
9325:
9313:
9309:
9305:
9302:
9291:
9288:
9286:
9284:
9279:
9275:
9271:
9268:
9265:
9264:
9261:
9256:
9252:
9248:
9241:
9235:
9230:
9220:
9216:
9212:
9206:
9200:
9195:
9188:
9185:
9180:
9176:
9172:
9167:
9163:
9159:
9156:
9154:
9150:
9146:
9142:
9141:
9138:
9133:
9129:
9125:
9122:
9117:
9114:
9110:
9106:
9103:
9100:
9095:
9091:
9087:
9084:
9081:
9078:
9075:
9070:
9066:
9062:
9059:
9057:
9055:
9050:
9046:
9042:
9039:
9036:
9035:
9011:
9006:
9002:
8998:
8995:
8992:
8983:
8978:
8974:
8967:
8963:
8959:
8923:
8919:
8893:
8889:
8885:
8880:
8876:
8872:
8867:
8863:
8859:
8854:
8850:
8826:
8820:
8815:
8808:
8802:
8799:
8774:
8771:
8767:
8763:
8758:
8755:
8751:
8730:
8708:
8704:
8673:
8669:
8664:
8660:
8655:
8647:
8643:
8638:
8634:
8629:
8621:
8618:
8611:
8605:
8600:
8592:
8589:
8583:
8580:
8577:
8574:
8571:
8568:
8563:
8559:
8553:
8550:
8546:
8540:
8532:
8528:
8520:
8515:
8512:
8508:
8503:
8500:
8498:
8494:
8490:
8486:
8485:
8478:
8474:
8469:
8465:
8460:
8452:
8448:
8443:
8439:
8434:
8426:
8423:
8416:
8410:
8405:
8397:
8394:
8388:
8385:
8382:
8379:
8376:
8373:
8368:
8364:
8358:
8355:
8351:
8345:
8337:
8333:
8325:
8320:
8317:
8313:
8308:
8305:
8303:
8299:
8295:
8291:
8290:
8259:
8255:
8232:
8228:
8224:
8219:
8215:
8192:
8188:
8165:
8161:
8138:
8134:
8107:
8103:
8098:
8095:
8092:
8089:
8086:
8083:
8077:
8072:
8068:
8062:
8058:
8054:
8049:
8045:
8039:
8035:
8031:
8028:
8023:
8019:
8015:
8012:
8009:
8006:
8000:
7997:
7991:
7985:
7980:
7976:
7971:
7967:
7946:
7943:
7928:
7924:
7920:
7915:
7911:
7907:
7902:
7898:
7894:
7889:
7885:
7862:
7859:
7853:
7847:
7842:
7835:
7832:
7829:
7824:
7820:
7816:
7811:
7807:
7803:
7800:
7796:
7793:
7787:
7781:
7776:
7769:
7766:
7763:
7758:
7754:
7750:
7745:
7741:
7737:
7734:
7712:
7692:
7667:
7663:
7659:
7656:
7636:
7616:
7594:
7590:
7567:
7563:
7540:
7535:
7529:
7524:
7520:
7517:
7511:
7505:
7501:
7495:
7490:
7486:
7482:
7477:
7473:
7448:
7444:
7423:
7417:
7414:
7411:
7408:
7405:
7402:
7399:
7391:
7386:
7378:
7374:
7370:
7367:
7364:
7361:
7358:
7355:
7352:
7349:
7346:
7343:
7338:
7334:
7330:
7327:
7324:
7321:
7315:
7309:
7304:
7297:
7291:
7286:
7282:
7277:
7273:
7252:
7249:
7232:
7208:
7184:
7173:Burgers vector
7160:
7136:
7114:
7110:
7083:
7079:
7051:
7047:
7041:
7037:
7032:
7027:
7022:
7018:
7013:
7005:
7001:
6997:
6992:
6987:
6983:
6979:
6974:
6970:
6964:
6960:
6953:
6948:
6944:
6919:
6915:
6911:
6906:
6902:
6890:Peierls stress
6875:
6871:
6844:
6840:
6817:
6813:
6782:
6778:
6774:
6750:
6746:
6742:
6737:
6733:
6728:
6723:
6720:
6715:
6707:
6703:
6697:
6693:
6687:
6683:
6677:
6672:
6664:
6660:
6654:
6650:
6644:
6641:
6637:
6629:
6621:
6617:
6609:
6605:
6601:
6594:
6590:
6587:
6580:
6576:
6572:
6566:
6561:
6555:
6549:
6544:
6516:
6512:
6488:
6482:
6477:
6456:
6453:
6450:
6426:
6422:
6418:
6415:
6409:
6404:
6400:
6394:
6389:
6385:
6382:
6379:
6376:
6373:
6370:
6367:
6361:
6356:
6352:
6349:
6327:
6298:
6294:
6282:Peierls stress
6263:
6240:
6236:
6215:
6212:
6209:
6206:
6203:
6200:
6178:
6174:
6153:
6147:
6142:
6138:
6135:
6113:
6109:
6084:
6080:
6076:
6071:
6067:
6040:
6036:
6033:
6028:
6024:
6019:
6012:
6008:
6003:
6000:
5997:
5994:
5991:
5988:
5981:
5977:
5974:
5971:
5965:
5959:
5954:
5947:
5942:
5938:
5934:
5931:
5925:
5920:
5916:
5913:
5908:
5904:
5899:
5895:
5892:
5889:
5886:
5880:
5874:
5869:
5862:
5856:
5851:
5847:
5842:
5838:
5816:
5813:
5800:
5797:
5794:
5774:
5771:
5766:
5762:
5735:
5731:
5708:
5704:
5681:
5674:
5668:
5663:
5635:
5629:
5626:
5621:
5590:
5585:
5581:
5577:
5572:
5568:
5564:
5552:
5547:
5543:
5539:
5536:
5533:
5522:
5517:
5513:
5495:
5489:
5486:
5481:
5464:
5458:
5453:
5439:
5434:
5427:
5421:
5416:
5386:
5383:
5380:
5377:
5374:
5371:
5368:
5365:
5362:
5335:
5329:
5324:
5293:
5288:
5264:
5258:
5254:
5248:
5244:
5240:
5237:
5234:
5230:
5225:
5221:
5216:
5209:
5203:
5198:
5190:
5187:
5184:
5181:
5178:
5175:
5171:
5166:
5160:
5156:
5149:
5144:
5140:
5137:
5134:
5131:
5127:
5123:
5120:
5117:
5114:
5108:
5102:
5097:
5090:
5084:
5079:
5075:
5070:
5066:
5035:
5031:
5018:
5015:
5010:
5009:
5006:
5003:
5000:
4997:
4974:
4970:
4945:
4921:
4917:
4913:
4909:
4905:
4902:
4890:
4887:
4873:
4867:
4844:
4838:
4814:
4788:
4781:
4778:
4775:
4772:
4769:
4766:
4763:
4760:
4757:
4752:
4750:
4747:
4746:
4741:
4738:
4735:
4731:
4727:
4723:
4719:
4716:
4709:
4706:
4700:
4693:
4680:
4674:
4669:
4665:
4653:
4648:
4645:
4639:
4633:
4632:
4630:
4625:
4619:
4616:
4608:
4605:
4587:
4584:
4580:Chaboche model
4562:
4541:
4519:
4515:
4492:
4488:
4484:
4480:
4476:
4473:
4470:
4467:
4464:
4459:
4454:
4447:
4443:
4439:
4434:
4429:
4423:
4420:
4412:
4409:
4375:
4372:
4369:
4349:
4326:
4323:
4317:
4305:plastic strain
4291:
4265:
4253:yield function
4240:
4237:
4234:
4231:
4228:
4225:
4201:
4194:
4191:
4188:
4185:
4182:
4179:
4176:
4173:
4170:
4165:
4163:
4160:
4159:
4156:
4153:
4150:
4146:
4142:
4138:
4134:
4131:
4123:
4120:
4115:
4107:
4103:
4091:
4088:
4072:
4060:
4056:
4052:
4048:
4044:
4041:
4030:
4029:
4027:
4022:
4013:
4009:
3997:
3994:
3978:
3965:
3961:
3957:
3953:
3949:
3945:
3942:
3938:
3926:
3920:
3917:
3909:
3906:
3888:
3885:
3884:
3883:
3880:
3868:
3865:
3835:
3831:
3827:
3823:
3818:
3813:
3808:
3803:
3795:
3792:
3789:
3785:
3781:
3774:
3768:
3765:
3759:
3754:
3749:
3745:
3741:
3737:
3733:
3730:
3727:
3721:
3718:
3707:
3704:
3698:
3692:
3686:
3683:
3675:
3672:
3665:
3659:
3651:
3648:
3641:
3635:
3632:
3626:
3624:
3619:
3615:
3611:
3607:
3602:
3597:
3592:
3587:
3579:
3576:
3573:
3569:
3565:
3558:
3554:
3545:
3542:
3536:
3530:
3524:
3518:
3513:
3509:
3505:
3503:
3484:
3481:
3456:
3452:
3448:
3445:
3441:
3437:
3430:
3427:
3424:
3418:
3411:
3406:
3402:
3398:
3394:
3390:
3387:
3384:
3378:
3375:
3364:
3361:
3355:
3349:
3343:
3340:
3311:
3307:
3303:
3300:
3296:
3292:
3285:
3282:
3279:
3273:
3264:
3260:
3256:
3242:
3238:
3226:
3223:
3219:
3213:
3210:
3207:
3202:
3194:
3182:
3178:
3174:
3163:
3153:
3141:
3130:
3124:
3121:
3110:
3107:
3101:
3095:
3089:
3086:
3057:
3054:
3051:
3046:
3038:
3026:
3022:
3018:
3007:
2997:
2985:
2974:
2966:
2954:
2924:
2896:
2892:
2888:
2885:
2881:
2877:
2870:
2867:
2864:
2860:
2856:
2847:
2843:
2839:
2825:
2821:
2809:
2806:
2802:
2793:
2781:
2770:
2764:
2761:
2750:
2747:
2741:
2735:
2729:
2726:
2718:
2715:
2708:
2702:
2694:
2691:
2684:
2678:
2675:
2669:
2667:
2662:
2658:
2654:
2651:
2647:
2643:
2636:
2633:
2630:
2626:
2622:
2613:
2608:
2604:
2600:
2598:
2547:
2544:
2515:
2510:
2505:
2502:
2492:
2486:
2481:
2476:
2473:
2461:
2458:
2451:
2445:
2440:
2437:
2410:
2407:
2404:
2377:
2374:
2366:
2363:
2334:
2308:
2305:
2297:
2294:
2282:
2279:
2276:
2271:
2264:
2261:
2253:
2250:
2241:
2235:
2227:
2224:
2221:
2217:
2183:
2180:
2177:
2153:
2149:
2145:
2140:
2134:
2131:
2123:
2120:
2113:
2105:
2102:
2099:
2073:
2070:
2067:
2062:
2054:
2041:
2036:
2031:
2026:
2021:
2009:
1999:
1987:
1976:
1970:
1967:
1959:
1956:
1926:
1923:
1919:
1913:
1910:
1906:
1900:
1894:
1890:
1886:
1880:
1876:
1871:
1866:
1861:
1856:
1835:
1811:
1808:
1805:
1800:
1791:
1786:
1781:
1776:
1771:
1758:
1747:
1742:
1739:
1736:
1714:
1694:
1667:
1655:
1644:
1638:
1635:
1627:
1624:
1616:
1609:
1606:
1598:
1595:
1585:
1582:
1578:
1555:
1552:
1547:
1543:
1522:
1519:
1514:
1509:
1486:
1483:
1467:
1464:
1438:
1435:
1411:
1408:
1395:
1392:
1384:
1380:
1366:
1361:
1321:
1317:
1303:
1298:
1281:
1278:
1272:
1266:
1263:
1255:
1251:
1235:
1232:
1226:
1220:
1182:
1178:
1164:
1159:
1142:
1139:
1133:
1127:
1119:
1115:
1099:
1093:
1087:
1054:
1043:
1039:
1023:
1020:
1014:
1008:
996:
988:
984:
968:
962:
956:
944:
936:
932:
918:
913:
881:
878:
877:
876:
864:
859:
854:
849:
845:
841:
836:
831:
826:
815:tertiary creep
811:
799:
794:
789:
784:
780:
776:
771:
766:
761:
746:
734:
729:
724:
719:
715:
711:
708:
705:
665:
662:
641:
638:
632:
607:
601:
574:
571:
565:
560:
554:
548:
543:
539:
525:
524:
517:
514:
481:
478:
477:
476:
473:
470:
462:
459:
447:thermodynamics
387:(1871) on the
372:
369:
368:
367:
364:
361:
358:
355:
352:
272:
268:
243:
238:
234:
230:
226:
222:
218:
213:
209:
205:
201:
198:
195:
192:
189:
186:
183:
179:
174:
170:
166:
162:
159:
156:
132:
123:parameter and
108:
84:
15:
9:
6:
4:
3:
2:
12802:
12791:
12788:
12786:
12783:
12782:
12780:
12768:
12764:
12760:
12756:
12752:
12745:
12738:
12734:
12730:
12726:
12722:
12715:
12708:
12704:
12700:
12696:
12692:
12688:
12681:
12674:
12670:
12666:
12662:
12658:
12654:
12650:
12643:
12636:
12632:
12628:
12624:
12620:
12616:
12609:
12603:
12597:
12590:
12586:
12582:
12578:
12574:
12570:
12569:
12564:
12557:
12555:
12547:
12543:
12539:
12535:
12534:
12526:
12519:
12515:
12511:
12507:
12502:
12497:
12493:
12489:
12488:
12480:
12473:
12469:
12465:
12461:
12457:
12453:
12449:
12445:
12444:
12436:
12429:
12425:
12421:
12417:
12413:
12409:
12405:
12401:
12400:
12395:
12388:
12381:
12377:
12373:
12369:
12368:
12363:
12356:
12354:
12346:
12342:
12338:
12334:
12330:
12326:
12325:
12320:
12313:
12311:
12303:
12299:
12295:
12291:
12287:
12283:
12279:
12275:
12274:
12266:
12264:
12249:
12245:
12244:
12239:
12232:
12230:
12228:
12220:
12216:
12212:
12208:
12204:
12200:
12199:
12191:
12189:
12174:
12167:
12160:
12158:
12143:
12137:
12134:, Macmillan,
12133:
12132:
12124:
12116:
12109:
12107:
12098:
12091:
12089:
12080:
12073:
12065:
12058:
12050:
12043:
12035:
12028:
12020:
12013:
12005:
11998:
11991:
11987:
11983:
11979:
11975:
11971:
11964:
11957:
11953:
11949:
11945:
11941:
11938:(in German),
11937:
11930:
11923:
11919:
11913:
11905:
11898:
11890:
11883:
11875:
11868:
11866:
11864:
11855:
11848:
11840:
11833:
11825:
11822:(in French),
11821:
11814:
11806:
11803:(in French),
11802:
11801:
11793:
11786:
11782:
11778:
11774:
11770:
11766:
11765:
11757:
11750:
11743:
11741:
11739:
11737:
11728:
11721:
11713:
11709:
11702:
11698:
11689:
11686:
11684:
11681:
11679:
11676:
11674:
11671:
11669:
11666:
11664:
11661:
11659:
11656:
11655:
11649:
11635:
11615:
11606:
11591:
11587:
11583:
11578:
11570:
11555:
11552:
11549:
11543:
11532:
11525:
11521:
11517:
11512:
11504:
11501:
11489:
11486:
11483:
11472:
11465:
11462:
11457:
11451:
11448:
11437:
11421:
11417:
11413:
11408:
11404:
11400:
11395:
11391:
11368:
11364:
11359:
11355:
11352:
11343:
11317:
11314:
11311:
11286:
11282:
11255:
11251:
11246:
11242:
11219:
11215:
11188:
11178:
11160:
11153:
11145:
11135:
11124:
11121:
11115:
11101:
11090:
11076:
11069:
11061:
11054:
11044:
11033:
11030:
11024:
11010:
10999:
10985:
10978:
10969:
10962:
10958:
10953:
10943:
10932:
10914:
10911:
10905:
10894:
10890:
10887:
10872:
10868:
10842:
10838:
10833:
10829:
10822:
10817:
10813:
10808:
10801:
10799:
10792:
10788:
10779:
10769:
10759:
10748:
10745:
10739:
10725:
10714:
10700:
10693:
10685:
10681:
10676:
10666:
10655:
10637:
10634:
10628:
10617:
10613:
10610:
10595:
10591:
10565:
10561:
10556:
10552:
10545:
10540:
10536:
10531:
10524:
10522:
10515:
10511:
10498:
10495:
10481:
10461:
10439:
10435:
10412:
10408:
10385:
10381:
10358:
10354:
10344:
10331:
10328:
10322:
10316:
10313:
10310:
10307:
10303:
10298:
10292:
10288:
10284:
10279:
10275:
10268:
10265:
10261:
10256:
10250:
10246:
10242:
10237:
10233:
10226:
10223:
10215:
10212:
10182:
10179:
10176:
10170:
10165:
10161:
10157:
10140:
10137:
10134:
10128:
10124:
10119:
10114:
10105:
10102:
10082:
10078:
10067:
10064:
10061:
10057:
10053:
10050:
10047:
10044:
10041:
10037:
10033:
10030:
10027:
10024:
10019:
10015:
10010:
10006:
10000:
9995:
9989:
9986:
9980:
9969:
9962:
9951:
9942:
9938:
9923:
9914:
9898:
9894:
9870:
9859:
9833:
9830:
9827:
9823:
9800:
9797:
9794:
9790:
9767:
9764:
9760:
9739:
9736:
9731:
9727:
9723:
9718:
9714:
9710:
9705:
9701:
9697:
9692:
9688:
9665:
9662:
9658:
9635:
9631:
9621:
9603:
9593:
9582:
9565:
9554:
9540:
9536:
9533:
9529:
9520:
9517:
9514:
9508:
9503:
9499:
9493:
9490:
9487:
9483:
9477:
9474:
9468:
9464:
9462:
9447:
9444:
9441:
9437:
9422:
9419:
9415:
9400:
9397:
9382:
9376:
9373:
9360:
9349:
9346:
9342:
9327:
9323:
9311:
9307:
9303:
9300:
9289:
9287:
9277:
9273:
9266:
9259:
9254:
9250:
9246:
9239:
9228:
9218:
9214:
9210:
9204:
9193:
9186:
9183:
9178:
9174:
9170:
9165:
9161:
9157:
9155:
9148:
9144:
9131:
9127:
9120:
9115:
9112:
9108:
9104:
9093:
9089:
9082:
9079:
9076:
9068:
9064:
9060:
9058:
9048:
9044:
9037:
9025:
9022:
9004:
9000:
8993:
8990:
8976:
8972:
8965:
8961:
8957:
8940:
8939:
8921:
8917:
8907:
8891:
8887:
8883:
8878:
8874:
8870:
8865:
8861:
8857:
8852:
8848:
8824:
8818:
8813:
8806:
8800:
8797:
8772:
8769:
8765:
8761:
8756:
8753:
8749:
8728:
8706:
8702:
8692:
8671:
8667:
8662:
8658:
8653:
8645:
8641:
8636:
8632:
8627:
8619:
8616:
8609:
8603:
8598:
8590:
8587:
8578:
8575:
8572:
8566:
8561:
8557:
8551:
8548:
8544:
8538:
8530:
8526:
8518:
8513:
8510:
8506:
8501:
8499:
8492:
8488:
8476:
8472:
8467:
8463:
8458:
8450:
8446:
8441:
8437:
8432:
8424:
8421:
8414:
8408:
8403:
8395:
8392:
8383:
8380:
8377:
8371:
8366:
8362:
8356:
8353:
8349:
8343:
8335:
8331:
8323:
8318:
8315:
8311:
8306:
8304:
8297:
8293:
8280:
8278:
8273:
8257:
8253:
8230:
8226:
8222:
8217:
8213:
8190:
8186:
8163:
8159:
8136:
8132:
8122:
8105:
8101:
8093:
8090:
8087:
8081:
8070:
8066:
8060:
8056:
8052:
8047:
8043:
8037:
8033:
8026:
8021:
8017:
8013:
8007:
8004:
7998:
7995:
7989:
7978:
7969:
7965:
7950:
7942:
7926:
7922:
7918:
7913:
7909:
7905:
7900:
7896:
7892:
7887:
7883:
7873:
7860:
7851:
7840:
7830:
7827:
7822:
7818:
7814:
7809:
7805:
7801:
7798:
7794:
7785:
7774:
7764:
7761:
7756:
7752:
7748:
7743:
7739:
7735:
7732:
7724:
7710:
7690:
7681:
7665:
7661:
7657:
7654:
7634:
7614:
7592:
7588:
7565:
7561:
7551:
7538:
7533:
7522:
7518:
7515:
7509:
7503:
7499:
7493:
7488:
7484:
7480:
7475:
7471:
7462:
7446:
7442:
7421:
7412:
7409:
7406:
7400:
7397:
7384:
7376:
7372:
7368:
7362:
7359:
7356:
7350:
7347:
7344:
7341:
7336:
7332:
7328:
7322:
7319:
7313:
7302:
7295:
7284:
7275:
7271:
7256:
7248:
7246:
7230:
7222:
7206:
7198:
7182:
7174:
7158:
7150:
7134:
7112:
7108:
7099:
7081:
7077:
7067:
7049:
7045:
7039:
7035:
7030:
7025:
7020:
7016:
7011:
7003:
6999:
6995:
6990:
6985:
6981:
6977:
6972:
6968:
6962:
6958:
6951:
6946:
6942:
6933:
6917:
6913:
6909:
6904:
6900:
6891:
6873:
6869:
6860:
6842:
6838:
6815:
6811:
6802:
6798:
6780:
6776:
6772:
6763:
6748:
6744:
6740:
6735:
6731:
6726:
6721:
6718:
6713:
6705:
6701:
6695:
6691:
6685:
6681:
6675:
6670:
6662:
6658:
6652:
6648:
6642:
6639:
6635:
6627:
6619:
6615:
6607:
6603:
6599:
6592:
6588:
6585:
6578:
6574:
6570:
6564:
6559:
6553:
6542:
6530:
6514:
6510:
6500:
6486:
6475:
6454:
6451:
6448:
6439:
6424:
6413:
6402:
6398:
6387:
6380:
6377:
6374:
6368:
6354:
6347:
6339:
6325:
6316:
6314:
6296:
6292:
6283:
6261:
6238:
6234:
6210:
6207:
6204:
6198:
6176:
6172:
6140:
6133:
6111:
6107:
6097:
6082:
6078:
6074:
6069:
6065:
6038:
6034:
6031:
6026:
6022:
6017:
6010:
6006:
5998:
5995:
5992:
5986:
5979:
5972:
5969:
5963:
5952:
5940:
5936:
5932:
5918:
5911:
5906:
5902:
5897:
5893:
5887:
5884:
5878:
5867:
5860:
5849:
5840:
5836:
5821:
5812:
5798:
5795:
5792:
5772:
5769:
5764:
5760:
5751:
5733:
5729:
5706:
5702:
5679:
5672:
5661:
5633:
5627:
5619:
5606:
5583:
5579:
5575:
5570:
5566:
5545:
5541:
5537:
5534:
5520:
5515:
5511:
5493:
5487:
5479:
5462:
5451:
5437:
5432:
5425:
5414:
5401:
5398:
5384:
5381:
5378:
5375:
5372:
5369:
5366:
5363:
5360:
5352:
5333:
5322:
5310:
5286:
5276:
5262:
5256:
5246:
5242:
5235:
5232:
5228:
5223:
5214:
5207:
5196:
5185:
5182:
5179:
5176:
5173:
5169:
5164:
5158:
5142:
5135:
5132:
5129:
5125:
5121:
5115:
5112:
5106:
5095:
5088:
5077:
5068:
5064:
5049:
5033:
5029:
5014:
5007:
5004:
5001:
4998:
4995:
4994:
4993:
4989:
4972:
4968:
4959:
4943:
4935:
4934:yield surface
4911:
4900:
4893:The quantity
4886:
4801:
4748:
4739:
4736:
4725:
4691:
4667:
4651:
4646:
4643:
4628:
4623:
4606:
4603:
4591:
4583:
4581:
4577:
4539:
4517:
4513:
4503:
4482:
4471:
4468:
4465:
4462:
4457:
4452:
4445:
4441:
4437:
4432:
4427:
4410:
4407:
4395:
4393:
4389:
4370:
4347:
4306:
4280:
4279:Cauchy stress
4254:
4235:
4232:
4229:
4223:
4214:
4161:
4154:
4151:
4140:
4129:
4089:
4070:
4050:
4039:
4025:
4020:
3995:
3976:
3963:
3951:
3940:
3936:
3924:
3907:
3904:
3892:
3881:
3878:
3877:
3876:
3874:
3873:small strains
3860:
3856:
3852:
3833:
3829:
3825:
3752:
3747:
3743:
3739:
3728:
3725:
3719:
3705:
3702:
3690:
3673:
3663:
3649:
3639:
3633:
3617:
3613:
3609:
3556:
3543:
3540:
3528:
3511:
3493:
3490:
3476:
3472:
3469:
3454:
3450:
3446:
3404:
3400:
3396:
3385:
3382:
3376:
3362:
3359:
3347:
3341:
3327:
3324:
3309:
3305:
3301:
3271:
3240:
3236:
3224:
3221:
3217:
3211:
3208:
3205:
3200:
3192:
3161:
3151:
3128:
3122:
3108:
3105:
3093:
3087:
3073:
3070:
3055:
3052:
3049:
3044:
3036:
3005:
2995:
2972:
2964:
2936:
2922:
2913:
2894:
2890:
2886:
2854:
2823:
2819:
2807:
2804:
2800:
2791:
2768:
2762:
2748:
2745:
2733:
2716:
2706:
2692:
2682:
2676:
2660:
2656:
2652:
2606:
2588:
2584:
2582:
2578:
2574:
2570:
2569:Bingham model
2566:
2565:Maxwell model
2562:
2552:
2539:
2535:
2531:
2513:
2500:
2490:
2484:
2471:
2459:
2456:
2449:
2443:
2435:
2422:
2408:
2405:
2402:
2394:
2364:
2361:
2349:
2322:
2295:
2280:
2277:
2274:
2269:
2251:
2248:
2239:
2233:
2225:
2222:
2219:
2206:
2204:
2199:
2197:
2194:the solid is
2181:
2178:
2175:
2166:
2151:
2147:
2143:
2138:
2121:
2118:
2111:
2103:
2100:
2097:
2089:
2086:
2071:
2068:
2065:
2060:
2052:
2007:
1997:
1974:
1957:
1942:
1924:
1921:
1917:
1911:
1908:
1904:
1898:
1888:
1878:
1833:
1824:
1809:
1806:
1803:
1798:
1756:
1745:
1740:
1737:
1734:
1726:
1712:
1692:
1683:
1665:
1642:
1625:
1596:
1583:
1580:
1567:
1553:
1550:
1545:
1541:
1520:
1517:
1512:
1491:
1482:
1465:
1436:
1422:
1418:
1407:
1393:
1390:
1382:
1341:
1337:
1319:
1279:
1276:
1264:
1261:
1253:
1201:
1198:
1180:
1140:
1137:
1125:
1117:
1068:
1065:
1052:
1041:
994:
986:
942:
934:
894:
886:
857:
847:
839:
834:
816:
812:
792:
782:
774:
769:
751:
747:
727:
717:
709:
706:
695:
694:primary creep
691:
690:
689:
686:
678:
670:
661:
659:
658:Perzyna model
588:
558:
541:
528:
522:
518:
515:
512:
511:
510:
508:
504:
500:
496:
486:
474:
471:
468:
467:
466:
461:Phenomenology
458:
456:
452:
448:
444:
440:
436:
431:
429:
428:Bingham solid
425:
421:
417:
413:
408:
406:
402:
401:primary creep
398:
394:
390:
386:
382:
378:
365:
362:
359:
356:
353:
350:
349:
348:
345:
343:
339:
335:
331:
327:
323:
319:
315:
311:
306:
304:
299:
298:yield surface
295:
290:
288:
270:
266:
257:
236:
232:
228:
220:
211:
207:
196:
193:
190:
187:
181:
172:
168:
157:
146:
130:
122:
106:
98:
82:
74:
70:
66:
62:
59:
54:
52:
47:
43:
39:
35:
31:
23:
19:
12758:
12754:
12744:
12728:
12724:
12714:
12690:
12686:
12680:
12656:
12652:
12642:
12618:
12614:
12608:
12596:
12572:
12566:
12537:
12531:
12525:
12491:
12485:
12479:
12447:
12441:
12435:
12403:
12397:
12387:
12374:(1): 81–93,
12371:
12365:
12328:
12322:
12277:
12271:
12252:, retrieved
12247:
12241:
12202:
12196:
12177:, retrieved
12172:
12145:, retrieved
12130:
12123:
12114:
12096:
12078:
12072:
12063:
12057:
12048:
12042:
12033:
12027:
12018:
12012:
12003:
11997:
11973:
11969:
11963:
11939:
11935:
11929:
11921:
11912:
11903:
11897:
11888:
11882:
11873:
11853:
11847:
11838:
11832:
11823:
11819:
11813:
11804:
11798:
11792:
11768:
11762:
11756:
11748:
11726:
11720:
11714:(2): 244–368
11711:
11707:
11701:
11607:
11438:
11179:
10499:
10496:
10345:
10216:
10213:
10192:shock regime
9924:
9920:
9622:
9026:
9023:
8941:
8908:
8693:
8281:
8274:
8123:
7951:
7948:
7874:
7725:
7682:
7552:
7463:
7257:
7254:
7068:
6934:
6764:
6531:
6501:
6440:
6340:
6317:
6098:
5822:
5818:
5607:
5402:
5399:
5277:
5050:
5020:
5011:
4990:
4892:
4802:
4592:
4589:
4579:
4575:
4504:
4396:
4391:
4386:denotes the
4215:
3893:
3890:
3870:
3853:
3494:
3486:
3470:
3328:
3325:
3074:
3071:
2937:
2914:
2589:
2585:
2581:Kelvin model
2576:
2572:
2560:
2557:
2532:
2423:
2323:
2207:
2200:
2196:viscoelastic
2167:
2090:
2087:
1943:
1825:
1727:
1684:
1568:
1496:
1413:
1342:
1338:
1202:
1199:
1069:
1066:
895:
891:
814:
749:
693:
683:
589:
529:
526:
492:
464:
432:
409:
381:Saint Venant
377:Henri Tresca
374:
346:
322:dislocations
307:
293:
291:
256:yield stress
55:
29:
28:
18:
12693:(1): 1–18,
12331:(5): 1816,
12205:(3): 1498,
11918:Prandtl, L.
11688:Quasi-solid
5351:strain-rate
424:strain rate
383:(1870) and
318:macroscopic
303:strain rate
287:strain rate
38:deformation
12779:Categories
12540:(2): 155,
12254:2009-05-13
12179:2009-05-13
12147:6 December
12117:, Springer
12099:, Springer
11841:, Elsevier
11694:References
6803:of length
4576:backstress
2395:rate, and
664:Creep test
285:) that is
73:frictional
12707:121579147
12673:137397027
12472:136118687
12428:136695336
12302:136966107
12175:: 541–547
11976:(1): 16,
11826:: 369–372
11807:: 754–756
11616:ρ
11571:ρ
11544:μ
11490:ρ
11487:π
11452:˙
11449:ξ
11347:^
11318:γ
11312:κ
11283:τ
11260:∞
11216:τ
11193:∞
11125:˙
11122:ξ
11116:γ
11102:˙
11091:ε
11034:˙
11031:ξ
11025:γ
11011:˙
11000:ε
10944:˙
10933:ε
10915:˙
10912:ξ
10906:γ
10891:
10882:^
10873:κ
10847:∞
10839:−
10823:−
10789:τ
10749:˙
10746:ξ
10740:γ
10726:˙
10715:ε
10667:˙
10656:ε
10638:˙
10635:ξ
10629:γ
10614:
10605:^
10596:κ
10570:∞
10562:−
10546:−
10512:τ
10462:θ
10436:τ
10409:τ
10355:τ
10329:−
10323:β
10317:
10308:φ
10299:α
10289:τ
10285:−
10276:τ
10266:β
10247:τ
10243:−
10224:α
10171:μ
10162:τ
10129:μ
10106:φ
10103:α
10083:ε
10079:θ
10068:−
10065:β
10062:−
10054:
10048:φ
10045:−
10034:
10028:α
10016:τ
9981:˙
9970:ε
9952:ε
9939:σ
9871:˙
9860:ε
9791:σ
9761:σ
9740:α
9659:θ
9632:θ
9594:˙
9583:ε
9566:˙
9555:ε
9537:
9509:μ
9438:σ
9416:σ
9401:
9383:α
9377:
9343:σ
9324:σ
9312:α
9304:
9274:σ
9247:−
9240:˙
9229:ε
9205:˙
9194:ε
9187:
9145:θ
9128:σ
9109:θ
9090:σ
9080:−
9065:θ
9045:σ
9038:θ
9001:σ
8994:θ
8977:ε
8962:σ
8918:σ
8825:˙
8814:ε
8801:˙
8798:ε
8620:˙
8617:ε
8610:˙
8599:ε
8591:
8567:μ
8514:−
8425:˙
8422:ε
8415:˙
8404:ε
8396:
8372:μ
8319:−
8277:Arrhenius
8254:μ
8187:σ
8160:σ
8133:σ
8102:μ
8082:μ
8067:σ
8044:σ
8018:σ
7999:˙
7996:ε
7979:ε
7966:σ
7923:β
7910:β
7897:α
7884:α
7852:˙
7841:ε
7831:
7819:β
7815:−
7806:β
7799:β
7786:˙
7775:ε
7765:
7753:α
7749:−
7740:α
7733:α
7711:β
7691:α
7562:σ
7523:ε
7485:σ
7472:σ
7443:σ
7410:α
7407:−
7401:
7385:ε
7360:β
7357:−
7351:
7333:σ
7314:˙
7303:ε
7285:ε
7272:σ
7221:kink loop
7183:ν
7078:ρ
7036:ρ
6991:ν
6959:ρ
6870:σ
6797:kink-pair
6745:σ
6741:≤
6732:σ
6719:−
6702:σ
6659:σ
6649:σ
6643:−
6589:
6554:˙
6543:ε
6511:σ
6476:ε
6449:β
6403:ε
6388:ε
6381:β
6355:ε
6293:σ
6262:σ
6235:μ
6199:μ
6173:σ
6141:ε
6108:σ
6079:σ
6075:≤
6066:σ
6039:σ
6035:≤
6023:σ
6007:μ
5987:μ
5964:˙
5953:ε
5937:σ
5919:ε
5903:σ
5879:˙
5868:ε
5850:ε
5837:σ
5765:∗
5680:∗
5673:˙
5662:ε
5634:˙
5620:ε
5576:−
5538:−
5516:∗
5494:˙
5480:ε
5463:˙
5452:ε
5433:∗
5426:˙
5415:ε
5334:˙
5323:ε
5287:ε
5247:∗
5236:−
5215:∗
5208:˙
5197:ε
5186:
5143:ε
5107:˙
5096:ε
5078:ε
5065:σ
5030:σ
4958:von Mises
4908:σ
4872:σ
4843:σ
4722:σ
4692:τ
4679:σ
4668:−
4664:σ
4644:−
4607:˙
4604:ε
4561:χ
4487:χ
4483:−
4479:σ
4411:˙
4408:ε
4374:⟩
4371:…
4368:⟨
4348:τ
4316:ε
4264:σ
4137:σ
4106:σ
4102:∂
4087:∂
4071:τ
4047:σ
4012:σ
4008:∂
3993:∂
3977:τ
3948:σ
3908:˙
3905:ε
3830:σ
3826:≥
3812:σ
3780:σ
3758:ε
3744:σ
3736:σ
3720:˙
3717:σ
3703:−
3674:˙
3671:ε
3650:˙
3647:ε
3634:˙
3631:ε
3614:σ
3596:σ
3564:ε
3553:σ
3541:−
3517:ε
3508:ε
3451:σ
3447:≥
3444:‖
3440:σ
3436:‖
3417:σ
3401:σ
3393:σ
3377:˙
3374:σ
3360:−
3342:˙
3339:ε
3306:σ
3302:≥
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3295:σ
3291:‖
3263:‖
3259:σ
3255:‖
3237:σ
3225:−
3209:−
3193:λ
3181:‖
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3152:λ
3140:σ
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3120:σ
3106:−
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3085:ε
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3025:‖
3021:σ
3017:‖
2996:λ
2984:σ
2965:η
2953:σ
2923:η
2891:σ
2887:≥
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2880:σ
2876:‖
2846:‖
2842:σ
2838:‖
2820:σ
2808:−
2792:η
2780:σ
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2760:σ
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2714:ε
2693:˙
2690:ε
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2646:σ
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2621:ε
2603:σ
2571:) or the
2514:˙
2509:¯
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2501:ϵ
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2365:˙
2362:ε
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2278:−
2252:˙
2249:ε
2203:isochoric
2122:˙
2119:ε
2104:λ
2098:σ
2069:−
2053:λ
2030:σ
1998:λ
1986:σ
1958:˙
1955:ε
1918:σ
1905:σ
1893:σ
1885:σ
1865:σ
1807:−
1780:σ
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1277:−
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1138:−
1092:ε
1013:ε
961:ε
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848:≤
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775:≤
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718:≤
714:ε
710:≤
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600:ε
564:ε
547:ε
538:ε
489:suddenly.
393:Von Mises
267:σ
208:ε
197:λ
191:σ
169:ε
158:σ
145:power-law
121:viscosity
107:λ
11920:(1924),
11652:See also
8938:Voce law
4453:⟩
4433:⟨
4392:Chaboche
3964:⟩
3937:⟨
2567:and the
2350:tensor,
1421:parallel
495:yielding
453:and the
422:and the
330:polymers
12623:Bibcode
12600:Schwer
12577:Bibcode
12518:2166303
12452:Bibcode
12408:Bibcode
12333:Bibcode
12282:Bibcode
12207:Bibcode
11978:Bibcode
11944:Bibcode
11773:Bibcode
11668:Dashpot
10427:at 0K,
7243:is the
7195:is the
7096:is the
6888:is the
6857:is the
5307:is the
4277:is the
2391:is the
2346:is the
412:Prandtl
371:History
338:bitumen
119:is the
95:is the
65:dashpot
58:Hookean
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590:where
503:strain
499:stress
416:Prager
336:, and
326:grains
314:alloys
310:metals
61:spring
12703:S2CID
12669:S2CID
12514:S2CID
12496:arXiv
12468:S2CID
12424:S2CID
12298:S2CID
12169:(PDF)
8279:form
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4251:is a
2168:When
685:Creep
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143:is a
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42:loads
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3348:=
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2240:3
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2220:=
2216:s
2179:=
2176:N
2152:N
2148:/
2144:1
2139:)
2133:p
2130:v
2112:(
2101:=
2072:1
2066:N
2061:]
2040:|
2035:|
2025:|
2020:|
2008:[
1975:=
1969:p
1966:v
1925:j
1922:i
1912:j
1909:i
1899:=
1889::
1879:=
1875:|
1870:|
1860:|
1855:|
1834:N
1810:1
1804:N
1799:]
1790:|
1785:|
1775:|
1770:|
1746:[
1738:=
1643:=
1637:p
1634:v
1608:p
1605:v
1581:=
1554:0
1551:=
1546:y
1521:0
1518:=
1513:e
1394:0
1391:=
1383:t
1379:d
1360:d
1320:t
1316:d
1297:d
1280:1
1271:E
1262:=
1254:t
1250:d
1234:p
1231:v
1219:d
1181:t
1177:d
1158:d
1141:1
1132:E
1126:=
1118:t
1114:d
1098:e
1086:d
1053:.
1042:t
1038:d
1022:p
1019:v
1007:d
995:+
987:t
983:d
967:e
955:d
943:=
935:t
931:d
912:d
875:.
863:)
858:R
835:2
825:(
810:.
798:)
793:2
770:1
760:(
745:.
733:)
728:1
707:0
704:(
640:p
637:v
606:e
573:p
570:v
559:+
553:e
542:=
271:y
258:(
242:]
237:N
233:/
229:1
225:)
221:t
217:d
212:/
204:d
200:(
194:=
188:=
185:)
182:t
178:d
173:/
165:d
161:(
155:[
131:N
83:E
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