Nucleation under multi-axial loading in variational phase-field models of brittle fracture

Phase-field models of brittle fracture can be regarded as gradient damage including an intrinsic internal length. This length determines the stability threshold solutions with homogeneous and thus strength material, is often tuned to retrieve experimental in uniaxial tensile tests. In this paper, we focus on multiaxial stress states show that available energy decompositions, introduced avoid crack interpenetration allow for unsymmetric behavior tension compression, lead surfaces different but fixed shapes. Thus, once scale tailored recover strength, it not possible match compressive or shear strength. We propose a new decomposition enables straightforward calibration multi-axial failure surface Drucker-Prager type. The decomposition, which hinges upon theory structured deformations, encompasses volumetric-deviatoric no-tension special cases. Preserving variational structure model, includes additional free parameter calibrated based ratio (or, if possible, strength), successfully demonstrated two data sets taken from literature.