Well-Posed Continuum Damage Models Without the Agonizing Gradient

Classical local damage models which represent softening behavior come with a serious bottleneck: Their computational response at component level depends on the used mesh, a result of the underlying mathematical ill-posedness of the localization phenomenon implied by softening. Traditional remedies include non-local or gradient-enhanced formulations which effectively preclude localization by introducing a suitable length scale. However, these formulations come with a few downsides: Integrating them into finite element (FE) codes is rather intrusive, they are not necessarily well-posed in terms of uniqueness and they cannot be up-scaled, i.e., homogenized. The alternative route via adding a viscous term nullifies the elastic region of the model. We discuss a damage-modeling approach based on measure theory, i.e., describing the distribution of "damaged mass". Based on the established framework of continuum thermodynamics, the model is formulated by specifying both the free energy and the dissipation in a direct way. The involved potentials are, by definition, convex, and lead to a well-posed mechanical problem. Put differently, the model leads to a mesh-independent response which may be computed in a numerically robust way. Moreover, due to their local nature, these models may be readily integrated into conventional user subroutines of industrial FE codes.