ON UNIQUENESS OF THE DYNAMIC FINITE-STEP PROBLEM IN GRADIENT-DEPENDENT SOFTENING PLASTICITY

The dynamic evolution of an elastoplastic softening solid is considere d. A material model including in the yield function the Laplacian of t he plastic multiplier is used to regularize the problem. The dynamic f inite;step problem is formulated according to a generalized mid-point integration scheme. Space discretization is carried out by a mixed fin ite element technique based on generalized variables. A sufficient uni queness condition of the finite-step solution is proved. For a one-dim ensional problem also a necessary and sufficient condition is presente d. A simple numerical test shows the regularizing properties (mesh-ind ependence) of the proposed model and the positive influence of the gra dient term also on the time step amplitude ensuring uniqueness of solu tion. Copyright (C) 1996 Published by Elsevier Science Ltd.