Analogy Between Body Force and Inelastic Strain Gradient in Cubic Crystals and Isotropic Bodies

Abstract

Physicists and engineers often encounter problems involving the stresses and strains in a body with a combination of elastic, creep and thermal, and plastic strains. Methods of analyzing elastic bodies subject to surface and body forces are more familiar to analysts than the corresponding analysis of inelastic bodies. It is the aim of the present note to show the analogy between the inelastic strain, which consists of a combination of thermal, creep, and plastic strains, and applied forces. This analogy is well known for thermal stresses. It is generalized here to include creep and plastic strain in both cubic crystals and isotropic media. Let rij and efj be the stress and strain components referred to a set of rectangular coordinates. The strain consists of the elastic strain et' and the inelastic strain ell' which is composed of thermal strain etj>, creep strain eij, and plastic strain ejj, so that e j = esj' + ej', (1) eljl = edij + eijj + eij, (2) Recently, T. Y. Thomas' has given a general compact form of the elastic stressstrain relationship in cubic crystals. This relationship has made possible the following simple formulation of the above-mentioned analogy for cubic crystals. Let a denote a crystal axis of the cubic crystal. Thomas has shown