A relaxation-based approach to damage modeling

Material models, including softening effects due to, for example, damage and localizations, share the problem of ill-posed boundary value problems that yield mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior described, for example, by internal variables, at a spatial level. This can take account of the gradient of the internal variable to yield mesh-independent finite element results. In this paper, we present a new approach to damage modeling that does not use common field functions, inclusion of gradients or complex integration techniques: Appropriate modifications of the relaxed (condensed) energy hold the same advantage as other methods, but with much less numerical effort. We start with the theoretical derivation and then discuss the numerical treatment. Finally, we present finite element results that prove empirically how the new approach works.