An efficient adaptive length scale insensitive phase-field model for three-dimensional fracture of solids using trilinear multi-node elements - Yue, Qiang; Wang, Qiao; Zhou, Wei; Rabczuk, Timon; Zhuang, Xiaoying; Liu, Biao; Chang, Xiaolin (International journal of mechanical sciences, 2023)
•An adaptive phase-field method is proposed based on trilinear multi-node elements.•The length scale insensitive phase-field model is combined with the adaptive method.•A robust adaptive criterion associated with the internal length scale is outlined.•Substantial computational memory and time required in phase-field modelling are reduced.•The method is successfully used to simulate simple and mixed-mode fracture in three-dimensional conditions. As a diffused fracture theory, phase-field models can seamlessly simulate complex crack patterns such as extending, branching, and merging. Despite the success of phase-field models, there are two issues in previous methods of three-dimensional (3-D) fracture. Firstly, the nonlinear governing equations lead to the huge computational costs, which hinder the application of phase-field models in 3-D problems. Secondly, these models, which are mostly developed based on a simple quadratic degradation function, provide numerical solutions that are sensitive to a length scale. Hence, this work addresses an efficient adaptive phase-field model with the aid of trilinear multi-node elements. The order of the elements remains constant with the increase of the number of nodes. As the mesh size and length scale significantly influence the numerical precision, a robust adaptive criterion is established in which the element refinement is controlled by both internal length scale and phase-field. According to the criterion, an expected mesh density in the failure domain can be obtained even for nonuniform initial mesh. Besides, being able to extend the phase-field regularized cohesive zone model, the adaptive model provides length scale insensitive responses for both crack path and peak load. The failure of brittle and quasi-brittle materials in three-dimensional conditions, including simple and mixed-mode fracture, can be simulated by the proposed model. Several benchmark examples are analyzed to show the efficiency and accuracy of the trilinear element-based adaptive phase-field model (TAPFM), and the results are compared with the standard phase-field model as well as experimental data. [Display omitted]