On the use of symmetry to simplify the constitutive equations of isotropic materials with memory

Abstract

This paper is concerned with general, compressible, isotropic materials, solid or fluid, characterized by functionals which give the stress when the history of the strain is specified. It is shown that for certain broad classes of motions the requirements of material symmetry and frame-indifference greatly simplify the form of constitutive equations. These simplifica­tions are derived without invoking integral expansions or other special hypotheses of smoothness for material response. Among the motions considered in detail are those which are locally equivalent to pure extensions and sheared extensions.