A continuous/discontinuous Galerkin formulation for a strain gradient-dependent damage model: 2D results, To appear Computational Mechanics

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 gradi-ents 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 of strain gradient-dependent problems is lacking. Here, a formulation is presented which allows the use of C0 nite element shape func-tions 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. Key words: damage, fracture, discontinuous Galerkin metho