How regularization concepts interfere with (quasi-)brittle damage: a comparison based on a unified variational framework

Abstract Three regularization concepts are assessed regarding their variational structure and interference with the predicted physics of (quasi-)brittle damage: fracture energy concept, viscous micromorphic regularization. They first introduced in a unified framework, depicting how they distinctively evolve from incremental minimization. The analysis certain time interval one-dimensional example is used to show retains well-posedness within softening regime. By way contrast, concept characterized by ill-posedness—as known previous non-variational analyses. Numerical examples finally demonstrate limitations capabilities each concept. ill-posed local leads its design spatially constant energy—in line Griffith’s theory. regularization, turn, yields well-posed problem but artificial viscosity can add bias unloading thickness. Furthermore, even more important, does not predict due locally heterogeneous loading rates. underlying this undesired dependency. However, it requires largest numerical efforts, since based on coupled two-field formulation.