On the crack-driving force of phase-field models in linearized and finite elasticity

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. •Discussion of various variational formulations in linear and finite elasticity.•Introduction of failure criteria based on physically motivated driving forces.•Investigation on the influences of the various parameters through parametric studies.•Numerical simulations of real-world problems by applying different failure criteria.•Demonstration of the superiority of the driving forces derived from fracture mechanics.