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204:, in the field. At the same time, much development occurred in the field – great improvements were achieved in technique, and the equipment was simplified. With refinements in the technology, photoelastic experiments were extended to determining three-dimensional states of stress. In parallel to developments in experimental technique, the first phenomenological description of photoelasticity was given in 1890 by
1047:
condition is achieved when the thickness of the prototype is much smaller as compared to dimensions in the plane. Thus one is only concerned with stresses acting parallel to the plane of the model, as other stress components are zero. The experimental setup varies from experiment to experiment. The two basic kinds of setup used are plane polariscope and circular polariscope.
263:
photoelasticity integrated with high-speed photography is utilized to investigate fracture behavior in materials. Another important application of the photoelasticity experiments is to study the stress field around bi-material notches. Bi-material notches exist in many engineering application like welded or adhesively bonded structures.
1090:
are added to the experimental setup of the plane polariscope. The first quarter-wave plate is placed in between the polarizer and the specimen and the second quarter-wave plate is placed between the specimen and the analyzer. The effect of adding the quarter-wave plate after the source-side polarizer
1063:
and a light source. The light source can either emit monochromatic light or white light depending upon the experiment. First the light is passed through the first polarizer which converts the light into plane polarized light. The apparatus is set up in such a way that this plane polarized light then
1050:
The working principle of a two-dimensional experiment allows the measurement of retardation, which can be converted to the difference between the first and second principal stress and their orientation. To further get values of each stress component, a technique called stress-separation is required.
1014:
For materials that do not show photoelastic behavior, it is still possible to study the stress distribution. The first step is to build a model, using photoelastic materials, which has geometry similar to the real structure under investigation. The loading is then applied in the same way to ensure
1046:
Photoelasticity can describe both three-dimensional and two-dimensional states of stress. However, examining photoelasticity in three-dimensional systems is more involved than two-dimensional or plane-stress system. So the present section deals with photoelasticity in a plane stress system. This
262:
embedded in an elastic medium. In the former case, the problem is nonlinear due to the contacts between bricks, while in the latter case the elastic solution is singular, so that numerical methods may fail to provide correct results. These can be obtained through photoelastic techniques. Dynamic
814:. Upon the application of stresses, photoelastic materials exhibit the property of birefringence, and the magnitude of the refractive indices at each point in the material is directly related to the state of stresses at that point. Information such as maximum
1098:
The basic advantage of a circular polariscope over a plane polariscope is that in a circular polariscope setup we only get the isochromatics and not the isoclinics. This eliminates the problem of differentiating between the isoclinics and the isochromatics.
958:
are the first and second principal stresses, respectively. The retardation changes the polarization of transmitted light. The polariscope combines the different polarization states of light waves before and after passing the specimen. Due to optical
219:– made possible by light-emitting diodes – continuous monitoring of structures under load became possible. This led to the development of dynamic photoelasticity, which has contributed greatly to the study of complex phenomena such as
1064:
passes through the stressed specimen. This light then follows, at each point of the specimen, the direction of principal stress at that point. The light is then made to pass through the analyzer and we finally get the fringe pattern.
456:
1455:
Kramer, Sharlotte; Beiermann, Brett; Davis, Douglas; Sottos, Nancy; White, Scott; Moore, Jeffrey (2013). "Characterization of
Mechanochemically Active Polymers Using Combined Photoelasticity and Fluorescence Measurements".
919:
1026:
Isochromatics are the loci of the points along which the difference in the first and second principal stress remains the same. Thus they are the lines which join the points with equal maximum shear stress magnitude.
663:
1067:
The fringe pattern in a plane polariscope setup consists of both the isochromatics and the isoclinics. The isoclinics change with the orientation of the polariscope while there is no change in the isochromatics.
251:. Digitization of polariscopy enables fast image acquisition and data processing, which allows its industrial applications to control quality of manufacturing process for materials such as glass and polymer.
1181:
Brewster, David (1816). "On the communication of the structure of doubly refracting crystals to glass, muriate of soda, fluor spar, and other substances, by mechanical compression and dilatation".
1489:
Fernandes, Cláudio P.; Glantz, Per-Olof J.; Svensson, Stig A.; Bergmark, Anders (2003). "Reflection photoelasticity: A new method for studies of clinical mechanics in prosthetic dentistry".
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1150:"Experiments on the depolarisation of light as exhibited by various mineral, animal, and vegetable bodies, with a reference of the phenomena to the general principles of polarisation"
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362:
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782:. Although the symmetric photoelastic tensor is most commonly defined with respect to mechanical strain, it is also possible to express photoelasticity in terms of the
778:. From either definition, it is clear that deformations to the body may induce optical anisotropy, which can cause an otherwise optically isotropic material to exhibit
522:
1095:
passing through the sample. The analyzer-side quarter-wave plate converts the circular polarization state back to linear before the light passes through the analyzer.
576:
1797:
Solaguren-Beascoa Fernández, M.; Alegre Calderón, J.M.; Bravo Díez, P.M.; Cuesta Segura, I.I. (2010). "Stress-separation techniques in photoelasticity: A review".
243:
Photoelasticity has been used for a variety of stress analyses and even for routine use in design, particularly before the advent of numerical methods, such as
1697:
Ayatollahi, M.R.; Mirsayar, M.M.; Dehghany, M. (2011). "Experimental determination of stress field parameters in bi-material notches using photoelasticity".
266:
For example, some elements of Gothic cathedrals previously thought decorative were first proved essential for structural support by photoelastic methods.
775:
196:, became a standard text on the subject. Between 1930 and 1940, many other books appeared on the subject, including books in Russian, German and French.
806:, as exhibited by certain transparent materials. Birefringence is a phenomenon in which a ray of light passing through a given material experiences two
370:
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and each component experiences a different refractive index due to the birefringence. The difference in the refractive indices leads to a relative
851:
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The same device functions as a plane polariscope when quarter wave plates are taken aside or rotated so their axes parallel to polarization axes
1011:
which depends on relative retardation. By studying the fringe pattern one can determine the state of stress at various points in the material.
584:
259:
1402:
Ajovalasit, A.; Petrucci, G.; Scafidi, M. (2012). "RGB photoelasticity applied to the analysis of membrane residual stress in glass".
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Several theoretical and experimental methods are utilized to provide additional information to solve individual stress components.
258:
Photoelasticity can successfully be used to investigate the highly localized stress state within masonry or in proximity of a
97:
1473:
1299:
69:
1240:
Fresnel, Augustin-Jean (2021). "Note on the double refraction of compressed glass". Translated by
Putland, Gavin Richard.
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materials, where two-dimensional photoelasticity is applicable, the magnitude of the relative retardation is given by the
212:
as the description by
Pockels only considered the effect of mechanical strain on the optical properties of the material.
1317:"Ueber die durch einseitigen Druck hervorgerufene Doppelbrechung regulärer Krystalle, speciell von Steinsalz und Sylvin"
76:
1627:
Noselli, G.; Dal Corso, F.; Bigoni, D. (2010). "The stress intensity near a stiffener disclosed by photoelasticity".
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116:
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Isoclinics are the loci of the points in the specimen along which the principal stresses are in the same direction.
50:
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83:
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205:
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Shukla, A. (2001). "High-speed fracture studies on bimaterial interfaces using photoelasticity—a review".
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passes through a photoelastic material, its electromagnetic wave components are resolved along the two
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176:. Experimental frameworks were developed at the beginning of the twentieth century with the works of
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model. Isochromatic fringe patterns around a steel platelet in a photo-elastic two-part epoxy resin.
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Laboratory for
Physical Modeling of Structures and Photoelasticity (University of Trento, Italy)
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and its orientation are available by analyzing the birefringence with an instrument called a
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1460:. Conference Proceedings of the Society for Experimental Mechanics Series. pp. 167–78.
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that the stress distribution in the model is similar to the stress in the real structure.
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Photoelastic experiment showing the internal stress distribution inside the cover of a
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is the symmetric part of the photoelastic tensor (the photoelastic strain tensor), and
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Application of
Imaging Techniques to Mechanics of Materials and Structures, Volume 4
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810:. The property of birefringence (or double refraction) is observed in many optical
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451:{\displaystyle \Delta (\varepsilon ^{-1})_{ij}=P_{ijk\ell }\partial _{k}u_{\ell }}
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Reprinted in H. de
Senarmont, E. Verdet, and L. Fresnel (eds.),
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783:
165:
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1526:"Localized stress percolation through dry masonry walls. Part I – Experiments"
1854:
1746:
Physical
Properties of Crystals: Their Representation by Tensors and Matrices
1675:
1565:"Localized stress percolation through dry masonry walls. Part II – Modelling"
1340:
1216:
Fresnel, Augustin (1822). "Note sur la double réfraction du verre comprimé".
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803:
779:
197:
169:
1354:
Nelson, D. F.; Lax, M. (1970). "New
Symmetry for Acousto-Optic Scattering".
914:{\displaystyle \Delta ={\frac {2\pi t}{\lambda }}C(\sigma _{1}-\sigma _{2})}
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208:, however this was proved inadequate almost a century later by Nelson &
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of the two waves, a fringe pattern is revealed. The number of fringe order
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retardation between the two components. Assuming a thin specimen made of
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Nonlinear Solid
Mechanics: Bifurcation Theory and Material Instability
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Tension lines in a plastic protractor seen under cross-polarized light
658:{\displaystyle \Delta (\varepsilon ^{-1})_{ij}=p_{ijk\ell }s_{k\ell }}
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252:
162:
1726:"The Canary: Michael Lewis on Chris Mark of the Department of Labor"
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172:. That diagnosis was confirmed in a direct refraction experiment by
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with respect to the deformation (the gradient of the displacement
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denotes differentiation with respect to the
Cartesian coordinate
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utilizes photoelasticity to analyze strain in denture materials.
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The photoelastic phenomenon was first discovered by the Scottish
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Leven, M.M.; Frocht, M.M., eds. (1969). "Vita Max Mark Frocht".
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1840:
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578:. For isotropic materials, this definition simplifies to
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1183:
Philosophical Transactions of the Royal Society of London
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Philosophical Transactions of the Royal Society of London
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Properties of Materials: Anisotropy, Symmetry, Structure
16:
Change in optical properties of a material due to stress
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The Journal of Strain Analysis for Engineering Design
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The Journal of Strain Analysis for Engineering Design
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The experimental procedure relies on the property of
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168:, who immediately recognized it as stress-induced
149:and is often used to experimentally determine the
524:is the linear displacement from equilibrium, and
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1836:University of Cambridge Page on Photoelasticity.
23:Plastic utensils in a photoelasticity experiment
1018:
320:{\displaystyle \Delta (\varepsilon ^{-1})_{ij}}
278:the change in the inverse permittivity tensor
1562:
1523:
1081:
1209:
1086:In a circular polariscope setup two quarter-
1281:
497:is the fourth-rank photoelasticity tensor,
1563:Bigoni, Davide; Noselli, Giovanni (2010).
1524:Bigoni, Davide; Noselli, Giovanni (2010).
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1001:{\displaystyle N={\frac {\Delta }{2\pi }}}
789:
1431:
1353:
1165:
924:where Δ is the induced retardation,
117:Learn how and when to remove this message
1569:European Journal of Mechanics – A/Solids
1530:European Journal of Mechanics - A/Solids
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357:{\displaystyle \partial _{\ell }u_{k}}
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1230:Oeuvres complètes d'Augustin Fresnel
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55:adding citations to reliable sources
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1724:Lewis, Michael (3 September 2024).
235:Photoelastic model to validate the
13:
1761:, Oxford University Press, 2005.
1748:, Oxford University Press, 1957.
1404:Measurement Science and Technology
1292:10.1016/B978-0-08-012998-3.50005-7
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1774:3rd ed., McGraw-Hill Inc., 1991
1629:International Journal of Fracture
1589:10.1016/j.euromechsol.2009.10.013
1550:10.1016/j.euromechsol.2009.10.009
1392:. J. Wiley and Sons, London, 1965
1075:Transmission Circular Polariscope
1059:The setup consists of two linear
1218:Annales de Chimie et de Physique
260:rigid line inclusion (stiffener)
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215:With the advent of the digital
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1606:. Cambridge University Press.
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1772:Experimental Stress Analysis,
1770:Dally, J.W. and Riley, W.F.,
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1424:10.1088/0957-0233/23/2/025601
1321:Annalen der Physik und Chemie
1286:. Pergamon. pp. xi–xii.
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544:{\displaystyle \partial _{l}}
1711:10.1016/j.matdes.2011.06.002
1466:10.1007/978-1-4419-9796-8_21
1019:Isoclinics and isochromatics
767:{\displaystyle P_{ijk\ell }}
738:. The antisymmetric part of
697:{\displaystyle p_{ijk\ell }}
490:{\displaystyle P_{ijk\ell }}
153:distribution in a material.
7:
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940:is the specimen thickness,
831:principal stress directions
190:Treatise on Photoelasticity
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1846:Build your own polariscope
1376:10.1103/PhysRevLett.24.379
1093:circularly polarized light
1082:Circular polariscope setup
727:{\displaystyle s_{k\ell }}
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145:. It is a property of all
1641:10.1007/s10704-010-9502-9
517:{\displaystyle u_{\ell }}
137:describes changes in the
1785:Digital Photoelasticity,
1676:10.1243/0309324011512658
1341:10.1002/andp.18902750313
1148:Brewster, David (1815).
932:stress-optic coefficient
1356:Physical Review Letters
1109:Acousto-optic modulator
1055:Plane polariscope setup
790:Experimental principles
192:, published in 1930 by
1866:Mechanical engineering
1811:10.1243/03093247JSA583
1699:Materials & Design
1261:Cite journal requires
1246:10.5281/zenodo.4706835
1232:, vol. 1 (1866),
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1167:10.1098/rstl.1815.0004
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186:University of London
51:improve this article
1731:The Washington Post
1602:Bigoni, D. (2012).
1581:2010EuJMA..29..299B
1542:2010EuJMA..29..291B
1416:2012MeScT..23b5601A
1368:1970PhRvL..24..379N
1333:1890AnP...275..440P
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1301:978-0-08-012998-3
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776:roto-optic tensor
270:Formal definition
249:boundary elements
206:Friedrich Pockels
131:materials science
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62:Find sources:
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40:This article
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1783:Ramesh, K.,
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816:shear stress
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227:Applications
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201:
189:
182:L.N.G. Filon
160:
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104:
94:
87:
80:
73:
61:
49:Please help
44:verification
41:
1433:10447/61842
1220:. Série 2.
1129:Polarimetry
1088:wave plates
820:polariscope
217:polariscope
143:deformation
1855:Categories
1744:J.F. Nye,
1189:: 156–78.
1135:References
1061:polarizers
1041:Jewel case
178:E.G. Coker
77:newspapers
1871:Mechanics
1819:208518298
1684:137504535
1224:: 376–83.
1203:108782967
1160:: 29–53.
993:π
986:Δ
900:σ
896:−
887:σ
875:λ
868:π
856:Δ
839:isotropic
760:ℓ
720:ℓ
690:ℓ
651:ℓ
638:ℓ
600:−
596:ε
589:Δ
533:∂
510:ℓ
483:ℓ
444:ℓ
430:∂
424:ℓ
386:−
382:ε
375:Δ
340:ℓ
336:∂
297:−
293:ε
286:Δ
253:Dentistry
237:stiffener
163:physicist
1805:: 1–17.
1649:56221414
1511:12543116
1442:53600215
1103:See also
812:crystals
221:fracture
1577:Bibcode
1538:Bibcode
1412:Bibcode
1364:Bibcode
1329:Bibcode
928:is the
734:is the
157:History
91:scholar
1876:Optics
1817:
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668:where
461:where
151:stress
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1680:S2CID
1645:S2CID
1438:S2CID
1199:S2CID
835:phase
827:light
98:JSTOR
84:books
1608:ISBN
1507:PMID
1470:ISBN
1296:ISBN
1267:help
951:and
180:and
70:news
1807:doi
1707:doi
1672:doi
1637:doi
1633:166
1585:doi
1546:doi
1499:doi
1462:doi
1428:hdl
1420:doi
1372:doi
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1191:doi
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1162:doi
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247:or
210:Lax
184:of
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