Phase-field finite deformation fracture with an effective energy for regularized crack face contact

Phase-field models are a leading approach for realistic fracture problems. They treat the crack as second phase and use gradient terms to smear out faces, enabling of standard numerical methods simulations. This regularization causes cracks occupy finite volume in reference, leads inability appropriately model closing or contacting -- without healing faces. Specifically, classical idealized face tractions that shear component is zero, normal zero when opens identical intact material closes. do not replicate this behavior. work addresses shortcoming by introducing an effective energy density endows regularized (finite volume) phase-field with properties sharp crack. The based on applying QR (upper triangular) decomposition deformation tensor basis crack, transparent identification modes. By then relaxing over those modes cost energy, obtained has response faces close open. A highlight it lies completely setting deformation, potential application soft materials other settings large rotations. applied numerically study representative complex loadings, including (1) cyclic loading cavity solid shows growth stress states; (2) pattern branching driven closure cracks.