Dynamic strain localization in elasto-(visco-)plastic solids, part 2. plane strain examples

Abstract

Viscoplasticity is introduced as a procedure to regularize the elastic-plastic solid, especially for those situations in which the underlying inviscid material exhibits instabilities which preclude meaningful analysis of the initial-value problem. The procedure is general and therefore has the advantage of allowing the regularization of any inviscid elastic-plastic material. Rate dependence is shown to naturally introduce a length-scale that sets the width of the shear bands in which the deformations localize and high strain gradients prevail. Then, provided that the element size is appropriate for an adequate description of the shear band geometry, the numerical solutions are shown to be pertinent. Stable and convergent solutions with mesh refinements are obtained which are shown to be devoid of spurious mesh length-scale effects. The numerical framework adopted for this study is realistic and relevant to the solution of large scale nonlinear problems. An efficient explicit time stepping algorithm is used to advance the solution in time, and low-order finite elements with only one stress-point are used. An unconditionally stable stress-point algorithm is used to integrate the nonlinear elasto-(visco-) plastic constitutive equations. Therefore, the only numerical restriction of the proposed computational procedure stems from a time step size restriction which emanates from the explicit time integration of the equations of motion. However, since the wave speeds remain elastic, this restriction is trivially dealt with, resulting in a most efficient computational procedure.