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An hp-adaptive discontinuous Galerkin method for phase field fracture [dataset] Open Access

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 hp-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 p-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.

Descriptions

Resource type

Dataset

Contributors

Creator: Bird, Robert ¹
Augarde, Charles E. ¹
Coombs, William M. ¹
Duddu, Ravindra ²
Giani, Stefano ¹
Huynh, Phuc T. ³
Sims, Bradley ¹

¹ Durham University, United Kingdom
² Vanderbilt University, USA
³ CIRTECH Institute, Vietnam

Funder

Engineering and Physical Sciences Research Council
European Commission
Royal Society
Office of Polar Programs

Research methods

Other description

Keyword

Phase field
Error estimation
hp-adaptivity
Discontinuous Galerkin
Fractures

Subject

Numerical analysis
Finite element method
Fracture mechanics

Location

Language

Cited in

Identifier

ark:/32150/r2pz50gw14x
doi:10.15128/r2pz50gw14x

Rights

Creative Commons Attribution 4.0 International (CC BY)

Publisher

Durham University

Date Created

2023

File Details

Depositor

R.E. Bird

Date Uploaded

11 August 2023, 15:08:23

Date Modified

14 August 2023, 11:08:15

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Characterization

File format: zip (ZIP Format)

Mime type: application/zip

File size: 31200

Last modified: 2023:08:11 16:42:27+01:00

Filename: Figure data An hp-adaptive discontinuous Galerkin method for phase field fracture [dataset].zip

Original checksum: 6030547472625efb4374bc5d320d1bed