Mixed Graph-FEM phase field modeling of fracture in plates and shells with nonlinearly elastic solids
Funding Number
2019KA03
Funding Sponsor
National Natural Science Foundation of China
Author's Department
Mechanical Engineering Department
Third Author's Department
Mechanical Engineering Department
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https://doi.org/10.1016/j.cma.2021.114282
Document Type
Research Article
Publication Title
Computer Methods in Applied Mechanics and Engineering
Publication Date
1-1-2021
doi
10.1016/j.cma.2021.114282
Abstract
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.
First Page
1
Last Page
25
Recommended Citation
APA Citation
Zhang, G.
Guo, T.
Elkhodary, K.
Tang, S.
&
Guo, X.
(2021). Mixed Graph-FEM phase field modeling of fracture in plates and shells with nonlinearly elastic solids. Computer Methods in Applied Mechanics and Engineering, 389, 1–25.
10.1016/j.cma.2021.114282
https://fount.aucegypt.edu/faculty_journal_articles/2830
MLA Citation
Zhang, Gang, et al.
"Mixed Graph-FEM phase field modeling of fracture in plates and shells with nonlinearly elastic solids." Computer Methods in Applied Mechanics and Engineering, vol. 389, 2021, pp. 1–25.
https://fount.aucegypt.edu/faculty_journal_articles/2830