Some observations on the regularizing field for gradient damage models

Gradient enhanced material models can potentially preserve well-posedness of incremental boundary value problems also after the onset of strain softening. Gradient dependent constitutive relations are rooted in the assumption that some scalar or tensor field, which appears in the yield function, has to be enriched by adding a term involving its second-order gradient field. For gradient-dependent plasticity this term is universally accepted to be the equivalent plastic strain. For gradient-dependent damage models different choices have been presented in the literature. They all possess the desired regularization of the solution, but they are not identical as regards the structural response. In this paper the implications of the choice of the regularization field are discussed. As an example a plasticity-like damage material model is formulated. Finally, a well-known one-dimensional problem is solved analytically, and the results are compared with results obtained via other gradient approaches.