An efficient adaptive length scale insensitive phase-field model for three-dimensional fracture of solids using trilinear multi-node elements

• Published in: International journal of mechanical sciences Vol. 253; p. 108351
• Main Authors: Yue, Qiang, Wang, Qiao, Zhou, Wei, Rabczuk, Timon, Zhuang, Xiaoying, Liu, Biao, Chang, Xiaolin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2023
• Subjects: Adaptive strategy; Fracture; Phase-field model; Three-dimensional modelling; Trilinear multi-node elements; Adaptive strategy; Phase-field model; Fracture; Trilinear multi-node elements; Three-dimensional modelling
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2023.108351

•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]