| Abstract Scope |
Phase-field fracture models are emerging as competitive approaches for realistic problems (e.g., heterogeneous materials, crack branching). They treat the crack as a second phase and use gradient terms to smear out the crack faces, enabling the use of standard numerical methods for simulations. However, a shortcoming of existing phase-field models is their inability to accurately model the response of cracks when the crack faces close due to compression. We develop an effective crack energy density, based on the QR decomposition of the deformation gradient, that gives the regularized phase-field crack the effective properties of an ideal sharp crack; that is, we obtain the intact material response when the crack faces are closed and zero energy when they are open. We apply our model to develop a homogenized description of fracture in layered composite rock (shale) under compression. |