Phase-field numerical strategies for deviatoric driven fractures

The phase-field approach regularizes the variational theory of fracture by approximating cracks with a smeared damage field. In this work, the attention is focused on those formulations approximating mode II fractures (shear fractures). In these models, only the deviatoric part of the strain elastic energy, penalized by the phase-field, drives the crack onset and evolution, whereas the elastic hydrostatic energetic contribution has no influence on the failure process. Consequently, cracks evolves according to the von Mises–Hencky–Hüber, also known as J2, failure criterion. Unfortunately, volumetric locking problem arises in the damaged zones if classical numerical solution strategies are adopted. As a consequence, damage localization bands appear with an excessive thickness, thus overestimating the fracture energy. In addition, the crack path geometry may be erroneously described because of the loss of precision of the displacement field in damaged zones. To circumvent these drawbacks, two numerical techniques are proposed, namely selective reduced integration and mixed displacement/pressure formulation, and their effectiveness evidenced by a numerical investigation.