Representation of Inelastic Mechanical Behavior by Means of State Variables

Summary

Previously introduced notion of the space of state and orientation is used to discuss the nature of differential equation representation of mechanical behavior in the presence of finite deformations. An initially isotropic material element loses some of its symmetry during the course of deformation so that, in general, only a small set of superimposed rigid-body rotations leave the state and orientation of the material invariant at a given time. This observation implies that the state and orientation of the material can, and probably must, be represented by a set of tensors of various rank. The general form of the law which governs the “growth” of these variables during the course of deformation is obtained. Applications of these general results to elasticity, viscoelasticity and plasticity are briefly discussed.