  The phase-field approach to fracture has been proven to be a mathematically
sound and easy to implement method for computing crack propagation with
arbitrary crack paths. Hereby crack growth is driven by energy minimization
resulting in a variational crack-driving force. The definition of this force
out of a tension-related energy functional does, however, not always agree with
the established failure criteria of fracture mechanics. In this work different
variational formulations for linear and finite elastic materials are discussed
and ad-hoc driving forces are presented which are motivated by general fracture
mechanical considerations. The superiority of the generalized approach is
demonstrated by a series of numerical examples.
