About Elastoplastic Nonlocal Formulations with Damage Gradients

FEM results of softening materials are well known to show pathological mesh dependency. The main goal of this work is to revisit and propose efficient nonlocal damage gradient enhanced formulations able to avoid mesh dependency in the context of elastoplastic damage models with destination to industrial applications. This formulation is presented and studied for simple tension tests, with various spatial discretizations. Numerical aspects and implementation in ABAQUS-standard environment are discussed. The structure of the nonlocal element needed for those formulations is presented. For a given set of meshes, the ability of the proposed formulation to control the size of the necking zone is studied. In the same time the independence of the global dissipation to the mesh size is checked. Theoretical and practical limits of the proposed approach are highlighted.