A continuous/discontinuous Galerkin formulation for a strain gradient-dependent damage model

Abstract

The numerical solution of strain gradient-dependent continuum problems has been hindered by continuity demands on the basis functions. The presence of terms in constitutive models that involve gradients of the strain field means that the $C^0$ continuity of standard finite element shape functions is insufficient. Despite a resurgence of research interest in strain gradient continuum models to represent micro-mechanical effects, a sound, effective and simple framework for the numerical solution of strain gradient-dependent problems is lacking. Here, a formulation is presented which allows the use of $C^0$ finite element shape functions for the solution of a prototype strain gradient-dependent damage model. The formulation is examined in two dimensions for the simulation of crack propagation. Particular attention is paid to the application of non-standard boundary conditions.