A discontinuous Galerkin method for strain gradient-dependent damage: Study of interpolations and convergence

A discontinuous Galerkin method has been developed for strain gradient-dependent damage. The strength of this method lies in the fact that it allows the use of C0 interpolation functions for continuum theories involving higher-order derivatives, while in a conventional framework at least C1 interpolations are required. The discontinuous Galerkin formulation thereby offers significant potential for engineering computations with strain gradient-dependent models. When using basis functions with a low degree of continuity, jump conditions arise at element edges which are incorporated in the weak form. In addition to the formulation itself, a detailed study of the convergence properties of the method for various element types is presented and an error analysis is undertaken. Numerical results of some one- and two-dimensional problems are presented and discussed.