Finite element implementation of gradient plasticity models Part I: Gradient-dependent yield functions

Abstract

Theories with intrinsic or material length scales find applications in the modeling of size-dependent phenomena such as, for example, the localization of plastic flow into shear bands. In gradient-type plasticity theories, length scales are introduced through the coefficients of spatial gradients of one or more internal variables. The present work undertakes the variational formulation and finite element implementation of two families of gradient-type plasticity models in which higher-order gradients of the state variables enter the yield function (in Part I) or the evolution equations for the state variables (in Part II). As an example, the application to a gradient-type version of the von Mises plasticity model is described in detail in the present paper. Numerical examples of localization under plane strain tension are considered using both the gradient-type (non-local) model, and its corresponding classical (local) counterpart. An important consequence of using the non-local model is that the numerical solution does not exhibit the pathological mesh-dependence that is evident when the standard von Mises model is used.