An hp-adaptive discontinuous Galerkin method for phase field fracture

Bird, Robert E.; Augarde, Charles E.; Coombs, William M.; Duddu, Ravindra; Giani, Stefano; Huynh, Phuc T.; Sims, Bradley

Abstract

The phase field method is becoming the de facto choice for the numerical analysis of complex problems that involve multiple initiating, propagating, interacting, branching and merging fractures. However, within the context of finite element modelling, the method requires a fine mesh in regions where fractures will propagate, in order to capture sharp variations in the phase field representing the fractured/damaged regions. This means that the method can become computationally expensive when the fracture propagation paths are not known a priori. This paper presents a 2D -adaptive discontinuous Galerkin finite element method for phase field fracture that includes a posteriori error estimators for both the elasticity and phase field equations, which drive mesh adaptivity for static and propagating fractures. This combination means that it is possible to be reliably and efficiently solve phase field fracture problems with arbitrary initial meshes, irrespective of the initial geometry or loading conditions. This ability is demonstrated on several example problems, which are solved using a light-BFGS (Broyden–Fletcher–Goldfarb–Shanno) quasi-Newton algorithm. The examples highlight the importance of driving mesh adaptivity using both the elasticity and phase field errors for physically meaningful, yet computationally tractable, results. They also reveal the importance of including -refinement, which is typically not included in existing phase field literature. The above features provide a powerful and general tool for modelling fracture propagation with controlled errors and degree-of-freedom optimised meshes.

Citation

Bird, R. E., Augarde, C. E., Coombs, W. M., Duddu, R., Giani, S., Huynh, P. T., & Sims, B. (2023). An hp-adaptive discontinuous Galerkin method for phase field fracture. Computer Methods in Applied Mechanics and Engineering, 416, Article 116336. https://doi.org/10.1016/j.cma.2023.116336

• Journal Article Type: Article
• Acceptance Date: Jul 31, 2023
• Online Publication Date: Aug 28, 2023
• Publication Date: 2023-11
• Deposit Date: Aug 4, 2023
• Publicly Available Date: Aug 29, 2024
• Journal: Computer Methods in Applied Mechanics and Engineering
• Print ISSN: 0045-7825
• Electronic ISSN: 1879-2138
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 416
• Article Number: 116336
• DOI: https://doi.org/10.1016/j.cma.2023.116336
• Public URL: https://durham-repository.worktribe.com/output/1712051
• Publisher URL: https://www.sciencedirect.com/journal/computer-methods-in-applied-mechanics-and-engineering