Elastoplastic Wave Propagation in a Rate-Sensitive Finite Rod Having a Thermal Gradient

In this paper, the problem of one-dimensional wave propagation in a bar of a thermally sensitive viscoplastic material is considered. A constitutive equation is developed which explicitly accounts for the thermal state in both the elastic and inelastic components of the strain rate. A computational technique is proposed for solving the governing hyperbolic system of equations. This technique is a synthesis of the finite-difference method and the method of characteristics, and utilizes the most attractive features of both for solving nonlinear problems involving the propagation of strong discontinuities. Some results are shown for the propagation of waves through both decreasing and increasing temperature fields.