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The Photoelastic Phenomenon

  • Chapter
Matrix Theory of Photoelasticity

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 11))

Abstract

In Chapter 2, where the electromagnetic theory of light was briefly described, the basic properties of the propagation of a light ray in a crystal were studied. It was shown that when a light ray enters a crystal, it splits into two rays that are linearly polarized at right angles to each other, which propagate with different velocities. The refractive index associated with each light ray in the crystal can be found by use of Fresnel’s ellipsoid, which shows, for any point in the crystal, the variation of refractive index with direction of the light ray. This splitting of rays into two rays that have mutually perpendicular polarizations results from a physical property of crystalline materials that is called optical birefringence or simply birefringence.

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References

  1. D. Brewster: Phil. Trans. R. Soc. London 105, 60 (1815);

    Google Scholar 

  2. D. Brewster: Phil. Trans. R. Soc. London 106, 156 (1816)

    Google Scholar 

  3. F. E. Neumann: Berichte Königl. Preuss. Akad. Wissensch. 1840;

    Google Scholar 

  4. F. E. Neumann: Abh. der Königl. Akad der Wissensch. Berlin Part II 50 (1841);

    Google Scholar 

  5. F. E. Neumann: Berichte Königl. Pogg. Ann. 54, 449 (1841)

    Google Scholar 

  6. J. C. Maxwell: Trans. R. Soc. Edinburgh 20, 87 (1853)

    Google Scholar 

  7. E. G. Coker, L. N. G. Filon: A Treatise on Photoelasticity 2nd. ed. (University Press, Cambridge 1957)

    Google Scholar 

  8. A. Mesnager: Compt. Rend. 155, 1071 (1912)

    MATH  Google Scholar 

  9. A. Mesnager: Ann. Ponts Chaussées 4, 129 (1901)

    Google Scholar 

  10. A. Mesnager: Compt. Rend. 190, 1249(1930)

    Google Scholar 

  11. P. S. Theocaris: “Phenomenological Analysis of Mechanical and Optical Behaviour of Rheo-Optically Simple Materials”, in The Photoelastic Effect and Its Applications, (IUTAM Symposium) ed. by J. Kestens (Springer, Berlin, Heidelberg, New York 1975) pp. 146–230

    Google Scholar 

  12. M. G. Wertheim: Compt. Rend. 32, 289 (1851);

    Google Scholar 

  13. M. G. Wertheim: Compt. Rend. 33, 576 (1851);

    Google Scholar 

  14. M. G. Wertheim: Compt. Rend. 35, 276 (1852);

    Google Scholar 

  15. M. G. Wertheim: Compt. Rend. Ann. Chim. Phys. III 40, 156 (1854)

    Google Scholar 

Books

  • Coker, E.G., Filon, L.N.G.: A Treatise on Photoelasticity, 2nd ed. (Cambridge University Press, Cambridge 1957) Chap.3, pp.181–295

    Google Scholar 

  • Ramachandran, G.N., Ramaseshan, S.: “Crystal Optics”, in Crystal Optics Diffraction ed. by S. Flügge, Encyclopedia of Physics, Vol. 25/1 (Springer, Berlin, Göttingen, Heidelberg 1961) pp.1–217

    Google Scholar 

  • Stein, R.S.: Rheo-Optics of Polymers, J. Pol. Sci., Pt. C, Polymer Symposia (Wiley-Interscience, New York 1964)

    Google Scholar 

Papers

  • Amba-Rao, C.L.: “Stress-Strain-Time-Birefringence Relations in Photoelastic Plastics with Creep”, “Reo-Optics of Polymers”. J. Polymer Sci., Pt. C., Pol. Symp. 5, 75–86 (1964)

    Google Scholar 

  • Arakawa, I.: On the determination of the stress-optical coefficient of bakelite with initial stress. Proc. Phys.-Math. Soc. Jpn. 117–136 (1923)

    Google Scholar 

  • Arthur, R.E.: Theory of photoelasticity and its application to problems of stress analysis. J. Roy. Aero. Soc. 47, 263–272 (1943)

    Google Scholar 

  • Baud, R.V.: Contribution to study of the effect of elliptical polarization upon energy transmission. J. Opt. Soc. Am. 21, 119–123 (1931)

    ADS  Google Scholar 

  • Bayoumi, S.E.A., Frankl, E.K.: Fundamental relations in photoplasticity. Br. J. Appl. Phys. 4, 306–310 (1953)

    ADS  Google Scholar 

  • Braybon, J.E.H.: A new method of measurement of the variation with wavelength of the refractive index and absolute stress optical coefficients of amorphous solids. Proc. Phys. Soc. London 63, 446–451 (1950)

    ADS  Google Scholar 

  • Brewster, D.: Additional observations on the optical properties and structure of heated glass and annealed glass drops. Phil. Trans. R. Soc. London 105, 1–8 (1815)

    Google Scholar 

  • Brewster, D.: On the effect of simple pressure in producing that species of crystallization which forms two oppositely polarised images and exhibits the complementary colours by polarised light. Phil. Trans. R. Soc. London 105, 60–64 (1815)

    Google Scholar 

  • Brewster, D.: On the laws which regulate the polarisation of light by reflexion from transparent bodies. Phil. Trans. R. Soc. London 105, 125–159 (1815)

    Google Scholar 

  • Brewster, D.: 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. Phil. Trans. R. Soc. London 106, 156–178 (1816)

    Google Scholar 

  • Brewster, D.: On the effects of compression and dilatation in altering the polarising structure of doubly refracting crystals. Phil. Trans. R. Soc. Edinburgh 8, 281–286 (1818)

    Google Scholar 

  • Brewster, D.: On the laws which regulate the distribution of the polarising force in plates, tubes, and cylinders of glass, that have received the polarising structure. Phil. Trans. R. Soc. Edinburgh 8, 353–371 (1818)

    Google Scholar 

  • Brewster, D.: On the production of regular double diffraction in the molecules of bodies by simple pressure with observations on the origin of the doubly refracting structure. Phil. Trans. R. Soc. London 120, 87–97 (1830)

    Google Scholar 

  • Brewster, D.: On the production of crystalline structure in crystallised powders, by compression and traction. Phil. Trans. R. Soc. Edinburgh 20, 555–559 (1853)

    Google Scholar 

  • Brinson, H.F.: Mechanical and optical viscoelastic characterization of hysol 4290. Exp. Mech. 8, 561–566 (1968)

    Google Scholar 

  • Canit, J.C., Berger, D., Billardon, M.: Mesure de variations d’indice par Polarimétrie. Opt. Acta 13, 255–270 (1966)

    ADS  Google Scholar 

  • Coleman, B.D., Dill, E.H.: Theory of induced birefringence in materials with memory. J. Mech. Phys. Solids 19, 215–243 (1971)

    ADS  MATH  Google Scholar 

  • Coleman, B.D., Dill, E.H.: “Photoviscoelasticity: Theory and Practice”, in Photoelastic Effect and Its Applications (IUTAM Symposium) ed. by J. Kestens (Springer, Berlin, Heidelberg, New York 1975) pp.455–505

    Google Scholar 

  • Daniel, I.M.: Quasi-static properties of a photoviscoelastic material. Exp. Mech. 5, 83–89 (1965)

    Google Scholar 

  • De Candia, F., Russo, R., Vittoria, V.: Mechanical and photoelastic properties of ehtylene-propylene copolymers related to chain microstructure. J. Phys. Chem. 80, 2961–2966 (1976)

    Google Scholar 

  • Dill, E.H.: “A Theory of Photothermoviscoelasticity”, Proc. 4th Int. Congr. Rheology, Pt. 2 (1963) pp.51–59

    Google Scholar 

  • Dill, E.H.: “A Theory of Photothermoviscoelasticity”, Proc. 4th Int. Congr. Rheologoy, Pt. 2 (1963) pp.51–59

    Google Scholar 

  • Dill, E.H.: On Phenomenological rheo-optic constitutive relations. J. Poly. Sei., Pt. C 5, 67–74 (1964)

    Google Scholar 

  • Dill, E.H.: “Photoviscoelasticity”, Proc. 4th Symp. Naval Structural Mechanics: Mechanics and Chemistry of Solid Propellants, ed. by A.C. Eringen et al. (Pergamon Press, New York 1967) pp.443–461

    Google Scholar 

  • Dill, E.H., Fowlkes, C.W.: Photoviscoelastic experiments I. Trend Eng. (Univ. Washington Publ.) 16, 5–9 (1964)

    Google Scholar 

  • Durelli, A.J.: Discussion of “The birefringent response of a potential photoelastic material with variable elastic properties. Exp. Mech. 16, 151–153 (1976)

    Google Scholar 

  • Favre, H.: Sur l’application de la théorie des erreurs à la résolution d’un système d’équations utilisé en photoélasticité. Rev. Opt. 34, 305–322 (1955)

    Google Scholar 

  • Feldman, A., Horowitz, D., Waxier, R.M.: Photoelastic constants of potassium chloride at 10.6 μm. J. Opt. Soc. Am. 67, 254 (1977)

    ADS  Google Scholar 

  • Filon, L.N.G.: On the dispersion in artificial double refraction. Phil. Trans. R. Soc. London A 207, 263–306 (1907)

    ADS  Google Scholar 

  • Filon, L.N.G.: On the temperature variation of the photoelastic effect in strained glass. Proc. R. Soc. London A 89, 587–593 (1912)

    ADS  Google Scholar 

  • Fijon, L.N.G., Jessop, H.T.: On the stress optical effect in transparent solid strained beyond the elastic limit. Phil. Trans. R. Soc. London A 223, 89–125 (1922–1923)

    ADS  Google Scholar 

  • Frocht, M.M., Cheng, Y.F.: “An Experimental Study of the Laws of Double Refraction in the Plastic State in Cellulose Nitrate-Foundations for Three-Dimensional Photoplasticity”, Proc. Int. Symp. on Photoelasticity, Illinois Inst, of Technology, Chicago, 1961, ed. by M.M. Frocht (Pergamon Press, New York 1963) pp.195–216

    Google Scholar 

  • Frocht, M.M., Thomson, R.A.: Experiments in mechanical and optical coincidence in photoplasticity. Exp. Mech. 1, 43–47 (1961)

    Google Scholar 

  • Ghaswala, S.K.: Elements of the theory of photoelasticity. Civ. Eng. Public Works Rev. 45, 237–238 (1950)

    Google Scholar 

  • Grishchenko, A.E., Myznikov, V.G., Afonin, S.N., Skazka, V.S.: Study of the photoelasticity of polymers in an oscillating mechanical field. Vysoko-molekulyarnye Soedineniya, Seriya B-Kratkie Soobshcheniya 19, 504–506 (1977) (in Russian)

    Google Scholar 

  • Hauret, G., Cao, X.A.: Determination of photoelastic constants in thiourea by brillouin scattering. Rev. Phys. Appl. (in French) 12, 995–997 (1977)

    Google Scholar 

  • Heller, W., Quimfe, G.: On the validity of the Langevin theory of orientation and the possibility of distinguishing between inherent and photoelastic anisotropy. Phys. Rev. 61, 382 (1942)

    ADS  Google Scholar 

  • Janeschitz-Kriegl, H., Wales, J.L.S.: “Streaming Double Refraction, a General Report”, in Photoelastic Effect and Its Applications (IUTAM Symposium), ed. by J. Kestens (Springer, Berlin, Heidelberg, New York 1975) pp.271–293

    Google Scholar 

  • Javornicky, J.: Concerning the double nature of birefringence in plastics, Exp. Mech. 3, 175–176 (1963)

    Google Scholar 

  • Kerr, J.: Experiments on the birefringent action of strained glass. Phil. Mag. 26, 321–342 (1888)

    MATH  Google Scholar 

  • Kiesling, E.: “Non Linear, Quasi Static Behavior of Some Photoelastic and Mechanical Model Materials”; Ph. D. Thesis, Mich. State Univ., Ann Arbor, Michigan (1966)

    Google Scholar 

  • Kuno, J.: Effect of the age of phenolite on the coefficient of photoelastic extinction. Phil. Mag. 23, 63–64 (1937)

    Google Scholar 

  • Lee, G.H.: “The Theory of the Photoelastic Effect”; Ph. D. Thesis, Cornell Univ. (1937)

    Google Scholar 

  • Mach, E.: Ober die temporäre Doppelbrechung der Körper durch einseitigen Druck. Ann. Phys. Chem., Ser. II 146, 313–316 (1872)

    ADS  Google Scholar 

  • Maxwell, J.C.: On double refraction in a viscous fluid in motion. Proc. R. Soc. London 22, 46–47 (1873)

    Google Scholar 

  • Mindlin, R.D.: Analysis of doubly refracting materials with circularly and elliptically polarized light. J. Opt. Soc. Am. 27, 288–291 (1937)

    ADS  Google Scholar 

  • Mindlin, R.D.: A mathematical theory of photoviscoelasticity. J. Appl. Phys. 20, 206–216 (1949)

    ADS  MATH  Google Scholar 

  • Mindlin, R.D.: “Rotation-Dependence of the Photoelastic Effect”, in Photoelastic Effect and Its Applications (IUTAM Symposium) ed. by J. Kestens (Springer, Berlin, Heidelberg, New York 1975) pp.376–388

    Google Scholar 

  • Mueller, H.: Theory of photoelasticity in amorphous solids. Physics 6, 179–184 (1935)

    ADS  Google Scholar 

  • Mueller, H.: The theory of photoelasticity. J. Am. Ceram. Soc. 21, 27–33 (1938)

    Google Scholar 

  • Nelson, D.F., Lax, M., Lazay, P.D.: “Electrodynamics of Photoelastic Media: Theory and Experiment”, in Photoelastic Effect and Its Applications (IUTAM Symposium) ed. by J. Kestens (Springer, Berlin, Heidelberg, New York 1975) pp.316–350

    Google Scholar 

  • Neumann, F.E.: Die Gesetze der Doppelbrechung des Lichtes in komprimierten und ungleichförmig erwärmten unkristallinischen Körpern. Abh. d. königl. Akad. d. Wissensch. Berlin, Pt. II, 1–254 (1841)

    Google Scholar 

  • Nishitani, T.: Birefringence of non-linear viscoelastic-plastic polymers. J. Phys. D: Appl. Phys. 10, 791–797 (1977)

    ADS  Google Scholar 

  • Noblet, A., Sylin, G., Vandaele-Dossche, M., Van Geen, R.: La birefringence mécanique différée de signe négatif et sa représentation analogique. Bull. Cl. Sci. Acad. R. Belg., Ser. 5e, Vol. L, 534–561 (1964)

    Google Scholar 

  • Pauthier-Camier, S.: “The Available Experimental Methods for Measuring Optical Properties of Matter”, in Photoelastic Effect and Its Applications (IUTAM Symposium) ed. by J. Kestens (Springer, Berlin, Heidelberg, New York 1975) pp.231–256

    Google Scholar 

  • Philippoff, W.: “The Present Stand of Rheo-Optics of Polymer Solutions”, Proc. 5th Congr. Rheology, Kyoto, 1968, ed. by S. Onogi, Vol. 4 (Univ. of Tokyo Press, Tokyo 1970) pp.3–12

    Google Scholar 

  • Pindera, J.T.: Remarks on properties of photoviscoelastic model materials. Exp. Mech. 6, 375–380 (1966)

    Google Scholar 

  • Pindera, J.T., Cloud, G.: On Dispersion of birefringence of photoelastic materials. Exp. Mech. 6, 470–480 (1966)

    Google Scholar 

  • Richard, T.G., Young, W.C.: The birefringent response of a potential photoelastic material with variable elastic properties. Exp. Mech. 15, 226–229 (1975)

    Google Scholar 

  • Rivlin, R.S., Smith, G.F.: Birefringence in viscoelastic materials. ZAMP 22, 325–339 (1971)

    ADS  MATH  Google Scholar 

  • Sapriel, J., Vacher, R.: Photoelastic tensor components of Gd2(MoO4)3. J. Appl. Phys. 48, 1191–1194 (1977)

    ADS  Google Scholar 

  • Shanker, J., Sharma, H.P., Sharma, O.P., Sharma, J.C.: Theory of the photoelastic effect in ZnO, ZnS, and CdS crystals. Solid State Commun. 22, 401–404 (1977)

    ADS  Google Scholar 

  • Shanker, J., Bakhshi, P.S., Sharma, O.P.: Theory of the photoelasticity of cuprous halides. Solid State Commun. 24, 217–219 (1977)

    ADS  Google Scholar 

  • Sharma, H.P., Shanker, J., Verma, M.P.: Effect of Lundqvist’s many-body potential on the photoelastic behavior of ionic crystals. Phys. Rev. B: Solid State 15, 4100–4102 (1977)

    ADS  Google Scholar 

  • Sharma, J.C., Sharma, H.P., Shanker, J.: Effect of the exchange charge polarization on the photoelastic behavior of diatomic crystals. Can. J. Phys. 55, 1510–1511 (1977)

    ADS  Google Scholar 

  • Soroka, V.V.: Dispersion of the photoelasticity. Sov. Phys.-Solid State 18, 366–367 (1976)

    Google Scholar 

  • Sugie, M., Tada, K.: A theory of the photoelastic coefficients and undamped values of the linear electrooptic coefficients. Jpn. J. Appl. Phys. 15, 257–263 (1976)

    ADS  Google Scholar 

  • Tada, K., Kikuchi, K., Sato, K.: Dispersion of photoelastic coefficients in ZnSe. Jpn. J. Appl. Phys. 16, 757–760 (1977)

    ADS  Google Scholar 

  • Theocaris, P.S.: “Viscoelastic Properties of Epoxy Resins Derived from Creep and Relaxation Tests at Different Temperatures”, Rpt. NSF-G 8188/3, Brown Univ. (1960)

    Google Scholar 

  • Theocaris, P.S.: A review of the rheo-optical properties of linear high polymers. Exp. Mech. 5, 105–114 (1965)

    Google Scholar 

  • Theocaris, P.S.: Dependence of the stress-optical coefficients on the mechanical and optical properties of polymers. J. Strain Anal. 8, 267–276 (1973)

    Google Scholar 

  • Theocaris, P.S.: “Phenomenological Analysis of Mechanical and Optical Behaviour of Rheo-Optically Simple Materials”, in Photoelastic Effect and Its Applications (IUTAM Symposium), ed. by J. Kestens (Springer, Berlin, Heidelberg, New York 1975), pp.146–230

    Google Scholar 

  • Tokuoka, T.: Theoretical investigation of birefringence deformation relations in photo-elasto-plasticity. Int. J. Solids Struct. 1, 343–350 (1965)

    Google Scholar 

  • Tokuoka, T.: Mechanical foundations of birefringence of photo-elastoplastic media. Int. J. Solids Struct. 2, 49–58 (1966)

    Google Scholar 

  • Tokuoka, T.: Mechanical foundations of birefringence of elastic media and viscous media. Int. J. Eng. Sci. 4, 23–40 (1966)

    Google Scholar 

  • Tokuoka, T.: A mathematical theory of birefringence of viscoelastic media. J. Phys. Soc. Jpn. 23 (2), 430–435 (1967)

    ADS  Google Scholar 

  • Tokuoka, T., Miyakawa, M.: “Birefringent Formula in Elastic-Plastic Deformation Region of High Polymer Solids”, Proc. 14th Jpn. Natl. Congr. Appl. Mech. (1964)pp.100–105

    Google Scholar 

  • Van Geen, R.E.: Non-coïncidence des singularités mécaniques et optiques. C.R. Acad. Sci. Paris 258, 5164–5166 (1964)

    MATH  Google Scholar 

  • Van Geen, R.E.: Deux phénomènes dus à la non-linéarité des relations contrainte-biréfringence. C.R. Acad. Sci. Paris 259, 999–1001 (1964)

    Google Scholar 

  • Van Geen, R.E.: Contribution à l’étude du mécanisme de la biréfringence mécanique. Bull. Cl. Sci. Acad. R. Belg. Ser. 5e, Vol. L, 869–892 (1964)

    Google Scholar 

  • Van Geen, R.E.: Effect photoélastique et matériaux adéquats en photoélasti-cimétrie. Sci. Techniques de l’Armement 45, 381–476 (1971)

    Google Scholar 

  • Vandaele-Dossche, M., Van Geen, R.E.: La biréfringence mécanique en lumière ultra-violette et ses applications. Bull. Cl. Sci. Acad. R. Belg., Ser. 5e, Vol. L, 125–141 (1964)

    Google Scholar 

  • Waxier, R.M., Horowitz, D., Feldman, A.: Precision interferometer for measuring photoelastic constants. Appl. Opt. 16, 20–22 (1977)

    ADS  Google Scholar 

  • Wertheim, M.G.: Memoire sur la polarisation chromatique produite par le verre, comprimé. C.R. Acad. Sci. 32, 289–292 (1851).

    Google Scholar 

  • Wertheim, M.G.: Note sur la double réfraction artificiellement produite dans des cristaux du système régulier, C.R. Acad. Sci. 33, 576–579 (1851).

    Google Scholar 

  • Wertheim, M.G.: Deuxième note sur la double réfraction artificiellement produite dans des cristaux du système régulier, C.R. Acad. Sci. 35, 276–278 (1852)

    Google Scholar 

  • Wertheim, M.G.: Mémoire sur la double réfraction temporairement produite dans les corps isotropes et sur la rélation entre l’élasticité mécanique et l’élasticité optique. Ann. Chim. Phys. III, 40, 156–221 (1854)

    Google Scholar 

  • Williams, M.L., Arenz, R.J.: The engineering analysis of linear photovisco-elastic materials. Exp. Mech. 4, 249–262 (1964)

    Google Scholar 

  • Wilson, C.A.C.: The influence of surface-loading on the flexure of beams. Phil. Mag. 32, 481–503 (1891)

    MATH  Google Scholar 

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  1. Athens National Technical University, Athens, Greece

    Professor Pericles S. Theocaris D.Sc. & Professor Emmanuel E. Gdoutos Ph.D.

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  1. Professor Pericles S. Theocaris D.Sc.
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Theocaris, P.S., Gdoutos, E.E. (1979). The Photoelastic Phenomenon. In: Matrix Theory of Photoelasticity. Springer Series in Optical Sciences, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-35789-6_6

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