Damage growth modeling using the Thick Level Set (TLS) approach: Efficient discretization for quasi-static loadings

The Thick Level Set (TLS) model is a damage model containing a non-local treatment that prevents from spurious localization issues. It also offers an automatic transition from damage to fracture. The TLS approach to model damage growth was first presented in Möes et al. [24] with a first numerical implementation for a time-dependent damage evolution law. In this paper, we propose some improvements in terms of discretization and explicit damage growth algorithms to obtain a robust, efficient and easy-to-implement model. These improvements include a simple and efficient variational formulation for computing the non-local quantities as well as the introduction of a so-called ramped Heaviside enrichment function to properly take into account the transition to cracks in fully damaged zones. We consider here a simple explicit formulation for quasi-static loadings, decoupling the elastic computation and the damage growth. The method is validated through standard benchmarks and compared to the Griffith’s fracture theory. The convergence of energy and displacement errors is observed. More complex computations including damage initiations are eventually performed.