Nonlocal constitutive models with gradients of internal variables derived from a micro/macro homogenization procedure Original Research Article

Finite element simulations involving strain softening materials or finite strains are faced with problems of loss of uniqueness and strain localization. If localization occurs, the size of the region where the strains concentrate is determined by the mesh size and no convergence can be obtained with mesh refinement. A non-local approach has been proposed recently by Andrieux et al. [15–16] in order to solve the problem. With this approach, spatial gradients of internal variables are incorporated in the macroscopic constitutive equations via a homogenization procedure. In this paper, this new formulation is investigated and numerical algorithms are presented for the onedimensional case. The results of the numerical simulations demonstrate that the size of the strain localization zone cannot be arbitrarily small anymore.