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

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 which involve gradients of the strain eld means that the C0 continuity of standard finite element shape functions is insucient. In this work, a continuous/discontinuous Galerkin formulation is developed to solve a strain gradient-dependent damage problem in a rigorous manner. Potential discontinuities in the strain eld across element boundaries are incorporated in the weak form of the governing equations. The per-formance of the formulation is tested in one dimension for various interpolations, which provides guidance for two-dimensional simulations.