Comparison of a phase-field model and of a thick level set model for brittle and quasi-brittle fracture

Abstract

This paper provides a comparison between one particular phase-field damage model and a thick level set (TLS) damage model for the simulation of brittle and quasi-brittle fractures. The TLS model is recasted in a variational framework, which allows comparison with the phase-field model. Using this framework, both the equilibrium equations and the damage evolution laws are guided by the initial choice of the potential energy. The potentials of the phase-field model and of the TLS model are quite different. TLS potential enforces a priori a bound on damage gradient whereas the phase-field potential does not. The TLS damage model is defined such that the damage profile fits to the one of the phase-field model for a beam of infinite length. The model parameters are calibrated to obtain the same surface fracture energy. Numerical results are provided for unidimensional and bidimensional tests for both models. Qualitatively, similar results are observed, although TLS model is observed to be less sensible to boundary conditions.