On the numerical and mesh-dependent parameters in a computationally enhanced phase-field fracture model coupled with a novel mesh refinement strategy

The phase-field method has been proven as a robust and computationally efficient approach to model the propagation of fractures in brittle solids. However, the performance of this technique in the context of finite element method can be questioned due to restrictions in the mesh structure and the element size to capture the fracture as a diffusive damaged region. This study is dedicated to developing a methodology for finding an appropriate length-scale parameter to model the fracturing process in a way that matches the physical character of failure in materials. The fracture process zone is chosen as the key feature in this study to propose relationships for estimating the length-scale parameter based on the tensile strength and cracking properties, and the robustness of the method is verified using experimental data. To employ the phase-field method in modelling large-scale domains and complex geometries, a novel mesh refinement strategy is developed to increase the computational efficiency based on predicting a corrected tensile strength limit depending on the element size to capture the crack-tip effectively. The proposed mesh refinement strategy reduces the computational effort significantly. Reliability and robustness of the developed relationships are successfully examined by simulating benchmark cases and comparisons with physically measured data.