Regularization of continuum damage mechanics models for 3-D brittle materials using implicit gradient enhancement

A well-known problem which arises in local damage models is that they suffer from mesh dependence and strain localization. In this study, we employ the non-local implicit gradient damage formulation for mesh sensitivity analysis of brittle materials. The basic concept of the non-local implicit gradient model is that the strain at a given point depends not only on the strain at that point but also on the nearby strain field. The local equivalent strain is replaced with a non-local equivalent strain, which is constructed by solving a system of partial differential equations (PDEs). We solve this system of PDEs using finite element method (FEM) and split-operator method which has been applied to 3-D microplane damage models. We extend this approach to continuum damage models and apply it to brittle material for three different loading experiments. In these examples, we demonstrate that the implementation of the implicit gradient damage model using the split-operator method can successfully be applied to complex, 3-D geometries requiring large-scale unstructured FEM meshes, and eliminate mesh dependence. In not all cases the simulations were able to obtain the desired fracture widths as this would require meshes at even smaller resolutions which is beyond our current computing capacity