Evaluating the development of elastic anisotropy with plastic flow

Abstract

It has been observed that many initially isotropic materials show the development of anisotropic elastic response after plastic flow. It is desirable to be able to model this change in the elastic properties as a function of the extent of plastic flow. This is particularly important when considering the traveling of waves in some glassy polymers that exhibit large differences in the wave moduli along the different directions resulting from unequal plastic flow in these directions. A thermodynamically based model of plasticity is developed and used to evaluate the elastic moduli associated with infinitesimal elastic deformations around the unloaded configuration. It is shown that for this model there are at least four independent material functions describing the elastic moduli of an initially isotropic material. These moduli are functions of the isotropic invariants of the right plastic Cauchy stretch tensor.