Bilinear Theories in Plasticity and an Application to Two-Dimensional Wave Propagation

Abstract

The Koehler and Seitz bilinear theory is generalized and related to a similar theory given by Swainger. It is shown that, in contradistinction to the corresponding Hencky theory, the generalized theory depends partially on the strain path, and further leads to linearization of the governing equations. An alternative form analogous to the generalized Hooke’s law is given. Displacement equations of motion for the bilinear model are derived and explicit expressions for plastic wave velocities obtained. Dynamic equations for cases previously considered in the literature are compared. As an application, the initial stress discontinuities for the problem of scattering of a plane compressional step wave by a rigid, perfectly dense cylinder are obtained.