A continuous/discontinuous Galerkin formulation for a strain gradient-dependent damage model: 2D results

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 eld means that the C0 continuity of standard nite element shape functions is insufcient. 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 strain gradient-dependent problems is lacking. Here, a formulation is presented which allows the use of C0 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.