A new finite element technique for a phase field model of brittle fracture

Phase field models for fracture employ a continuous field variable to indicate cracks. The width of the transition zone between cracked and uncracked areas is controlled by a regularization parameter. The numerical implementation of such models is sensible to the choice of this parameter in conjunction with the mesh size, as the mesh has to be fine enough to resolve high gradients of the crack field appearing in the transition zones. This is the main computational limit and challenge of the implementation. To overcome this limitation, a finite element method using exponential shape functions is introduced. Numerical examples show that these new shape functions perform better than standard Lagrange shape functions.