Numerical assessment of thick level set models for quasi-brittle materials

Simulations of local damage models are known to be pathologically dependent on the mesh for a softening material behaviour (i.e. when the stress decreases for an increasing strain). Mesh independent solutions can be recovered using a non-local regularisation of the model (e.g. of the integral [1] or of the gradient-enhanced [2] type). With this kind of regularised models a parameter lc representing a characteristic length of the material is added to the other parameters of the model. This parameter enforces the width of the damaged band cutting through the material and is connected to the energy that is globally dissipated by the fracturing process.