Ideal Solids and Liquids Constitutive Equations

6 Effect of Symmetry on the Relationships Between the Stress and Strain 

7 Generalized Stress-Strain Hooke s Law for Isotropic Solids 162 

9 Generalized Strain-Stress Relationships for Ideal Elastic Systems 170 

The response of most materials to mechanical, electrical, optical and other force fields is time-dependent. The study of the responses to these force fields allows one to determine, respectively, the rheological, dielectrical and birefringence properties of materials. According to the second law of thermodynamics, part of the input energy involved in the perturbation must invariably be dissipated, and part of it is stored. It should be pointed out 

Both E, in ideal solids, and rj, in ideal liquids, are material functions independent of the size and shape of the material they describe. This holds for isotropic and homogeneous materials, that is, materials for which a property is the same at all directions at any point. Isotropic materials are so characterized because their degree of symmetry is infinite. In contrast, anisotropic materials present a limited number of elements of symmetry, and the lower the number of these elements, the higher the number of material functions necessary to describe the response of the material to a given perturbation. Even isotropic materials need two material functions to describe in a generalized way the relationship between the perturbation and the response. In order to formulate the mechanical behavior of ideal solids and ideal liquids in terms of constitutive equations, it is necessary to establish the concepts of strain and stress. 

---