On uniqueness of the dynamic finite-step problem in gradient-dependent softening plasticity

The dynamic evolution of an elastoplastic softening solid is considered. A material model including in the yield function the Laplacian of the plastic multiplier is used to regularize the problem. The dynamic finite-step problem is formulated according to a generalized mid-point integratron scheme. Space discretization is carried out by a mixed finite element technique based on generalired variables. A sutIicient uniqueness condition of the finite-step solution is proved. For a one-dimensional problem also a necessary and sufficient condition is presented. A simple numerical test shows the regularizing properties (mesh-independence) of the proposed model and the positive influenoe of the gradient term also on the time step amplitude ensuring uniqueness of solution. Copyright 0 1996 Published by Elsevier Science Ltd