A continuum level-set model of fracture

This work is devoted to the modeling of brittle and ductile fracture under the use of the level-set method. Within the proposed model a level-set function is taken as a smooth function that represents brittle damage in an implicit manner, that is the zero level-set of the continuous function coincides with the boundaries of the damage. Under the utilization of a regularization parameter that can be interpreted as a material’s internal length, crack faces of zero width are replaced by interfaces of finite width scaled by the length parameter. An energy functional is adopted and after following a variational field approach the equations of damage nucleation and propagation are revealed. Simple numerical examples indicate that the proposed level-set model is in good agreement with other successful models for brittle fracture. Moreover, ductile fracture is successfully captured by introducing an additional level set function so as to describe three distinct phases within the body: the damaged area, the rigid-perfectly plastic region and the elastic region. A simple example of damage propagation provides the behavior of a ductile material.