An adaptive isogeometric phase-field method for brittle fracture in rock-like materials

Abstract

In recent years, the phase-field method (PFM) has gained considerable attention to model fracture process. This is because, in a single framework, the method allows to model crack nucleation, growth, coalescence and branching. In addition, existing FE codes can be used with minimal modifications. However, one of the major limitations of the PFM is that, it requires extremely fine mesh to accurately capture the fracture process. An adaptive phase-field method within the framework of isogeometric analysis is presented in this work to model tensile and compressive-shear crack propagation in rock-like materials. Locally refined NURBS are adopted for describing both the geometry and the field variables. The local refinement is performed by structured mesh refinement strategy based on an error indicator that depends on the user-defined threshold value for the phase-field variable. Two phase-field models are adopted for simulating tensile and compressive-shear fractures in rock-like materials. For numerical implementation, a hybrid formulation combined with a staggered solution scheme is adopted. Several two-dimensional benchmark problems are investigated to demonstrated the robustness of the proposed framework. From the numerical study, it can be found that the developed adaptive framework achieves results comparable to a uniformly refined mesh with higher degrees of freedom.