Novel numerical strategy for solving strongly coupled elastoplastic damage models with explicit return algorithms: Application to geomaterials

We propose a numerical strategy for the explicit computation of a strongly-coupled formulation of an elastoplastic damage model that includes hardening and softening. We use a yield surface and a damage surface to calculate plastic deformation and damage growth. Our algorithm combines a coupled two surface elastoplastic damage model with an explicit return algorithm using thermodynamic conjugated forces. Drift from the yield- and damage- surfaces are typically neglected in strongly coupled two-surface plastic damage models. Our results show that these drifts are significant and they may lead to unphysical damage states, and thus they need to be prevented using return algorithms. Our proposed numerical strategy considers four possible cases: purely elastic deformation, elastic damage, purely plastic deformation, and plastic damage. We use an elastic predictor-plastic corrector scheme as a base and divide any predictor step into the contributions from the elastic and plastic components, where the elastic and plastic damage contributions are tested separately. We implement the model using a finite-difference scheme on a staggered grid. We validated the functionality of the model and algorithm in several tests and comparisons with previously reported experimental data. The numerical results agreed very well with the experimental data and they also demonstrated that numerical drift from the yield and damage surface was prevented.