An energetically consistent tension–compression split for phase-field models of fracture at large deformations

The predictive description of fracture has been an important topic of research over the last decades. In this context, the recently developed phase-field approach to fracture has proven to be an efficient and versatile tool in handling arbitrary and topologically complex crack patterns in an adequate manner. However, open problems reside in the distinction between tensile and compressive states in the framework of energetically driven crack evolution, especially at finite deformations. In the present contribution, a novel methodology to split energy-density functions is proposed that can be applied to a large variety of polyconvex energies. The applicability of the proposed formulation is validated by a series of numerical examples involving small and large deformations, in which we also provide comparisons with existing splits from literature. •Novel methodology to split hyperelastic energy-density functions in the context of phase-field fracture for finite deformations.•The model is suitable for a wide class of free-energy functions described by the invariants of the deformation tensor.•Applicability to some typical polyconvex energy functions is demonstrated by a range of numerical examples.