Mixed Graph-FEM phase field modeling of fracture in plates and shells with nonlinearly elastic solids

• Published in: Computer methods in applied mechanics and engineering 2022-02, Vol.389, p.114282, Article 114282
• Main Authors: Zhang, Gang, Guo, Tian Fu, Elkhodary, Khalil I., Tang, Shan, Guo, Xu
• Format: Article
• Language: English
• Subjects: Differential geometry; Discretization; Finite element method; Fracture; Graph; Mathematical models; Phase field; Plates; Robustness (mathematics); Shell
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2021.114282

This paper presents a mixed Graph-FEM (Finite Element Method) approach for the phase field modeling of fracture in plates and shells composed of nonlinearly elastic solids. In this approach, the finite element mesh is deemed equivalent to a typical graph in computer science. The equation for phase field evolution is thus discretized by a graph Laplacian on a curved surface. A corresponding solver is herein developed, considering the matrix sparsity of the discretized system, and constraining irreversible phase field variables (to values greater than zero and less than one). An alternating solution strategy between mechanical equilibrium and the phase field equation is proposed. Our method is then applied to the fracture of plates and shells of arbitrary curvature, exhibiting fast convergence and robustness compared with our previous work, as could be concluded from the several numerical benchmarks we performed. This method opens a new way to efficiently model the fracture of plates and shells, while utilizing conventional shell elements. •A phase-field modeling method is built to model the fracture of plates and shells with homogeneous materials.•A solver suitable for solving the discretized phase-field equation is developed.•The proposed method can be extended to study fracture of shells of heterogeneous materials.