Nonlocal large deformation and localization behavior of metals

The present paper deals with a nonlocal continuum plasticity model which in cludes the dependence of the yield function on a nonlocal equivalent plasti c strain measure. Particular attention is focused on the formulation of a g eneralized J(1)-J(2) yield criterion to describe the effect of hydrostatic stress on the plastic now properties of metals. and the nonlocal equivalent plastic strain is defined as a weighted average of the corresponding local measure taken over the neighboring material points of the body. The nonloc al yield condition leads to a partial differential equation which is solved rising the finite difference method at each iteration of a loading step, S ince this requires no additional boundary conditions. the displacement-base d finite element procedure is governed by the standard principle of virtual work, and the associated linearized variational equations are obtained in the usual manner from a consistent linearization algorithm. Numerical simul ations of the elastic-plastic deformation behavior of ductile metal specime ns show the influence of the various model parameters on the deformation an d localization prediction. The proposed nonlocal theory preserves well-pose dness of the governing equations in the post-localization regime and preven ts pathological mesh sensitivity of the numerical results. The internal len gth scale incorporated in the model determines the size of the localized sh ear bands. (C) 2001 Elsevier Science Ltd. All rights reserved.