Photoviscoelasticity

Abstract

The basic mathematical theory of the problem of photoviscoelasticity was given by R. D. Mindlin [20] (1949) in his well-known paper “A Mathematical Theory of Photo-Viscoelasticity”. He considered the time dependent relations between three second rank tensors: birefringence, stress, and strain. His emphasis was mainly upon the conditions under which a viscoelastic model material could be used to deduce the elastic stress distribution in a prototype. Upon assuming elastic volume change he found that, if the material was incompressible.and the loading was proportional (i.e. no variation in the distribution pattern of the load but only a magnitude change with the time), that in the relations

EquationSource<math display=&#x2019;block&#x2019;> <mtable columnalign=&#x2019;left&#x2019;> <mtr> <mtd> <mi>n</mi><mo>=</mo><msub> <mi>c</mi> <mi>&#x03C3;</mi> </msub> <mrow><mo>(</mo> <mrow> <msub> <mi>&#x03C3;</mi> <mn>1</mn> </msub> <mo>&#x2212;</mo><msub> <mi>&#x03C3;</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo></mrow><mo>=</mo><mn>2</mn><msub> <mi>c</mi> <mi>&#x03C3;</mi> </msub> <msub> <mi>&#x2113;</mi> <mrow> <mi>max</mi></mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mi>n</mi><mo>=</mo><msub> <mi>c</mi> <mi>&#x03B5;</mi> </msub> <mrow><mo>(</mo> <mrow> <msub> <mi>&#x03B5;</mi> <mn>1</mn> </msub> <mo>&#x2212;</mo><msub> <mi>&#x03B5;</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo></mrow><mo>=</mo><msub> <mi>c</mi> <mi>&#x03B5;</mi> </msub> <msub> <mi>&#x03B3;</mi> <mrow> <mi>max</mi></mrow> </msub> </mtd> </mtr> </mtable> </math>]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$\begin{gathered} n = {c_\sigma }\left( {{\sigma _1} - {\sigma _2}} \right) = 2{c_\sigma }{\ell _{\max }} \hfill \\ n = {c_\varepsilon }\left( {{\varepsilon _1} - {\varepsilon _2}} \right) = {c_\varepsilon }{\gamma _{\max }} \hfill \\ \end{gathered} $$

the stress-optical and the strain-optical constants are viewed as time dependent operators characteristic of the material. The polarizing axes and the principal axes were aligned in this case.