Robert Bird
PDRA
Durham University, UK

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, 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 presentation will discuss a 2D hp-adaptive discontinuous Galerkin finite element method for phase field where the coupled equations are solved using the light-BFGS (Broyden–Fletcher–Goldfarb–Shanno) quasi-Newton algorithm.  The adaptivity is driven by a posteriori error estimators for both the elasticity and phase field equations. Examples will be used to show the importance of driving mesh adaptivity using both errors estimators for physically meaningful, yet computationally tractable, results. Additionally, the examples highlight the importance of including p-refinement which reduces the need for small elements along the crack, this is typically not included in most of the existing phase field literature.  The combination of the above numerical methods 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 provides a powerful and general tool for modelling fracture propagation with controlled errors and degree-of-freedom optimised meshes.

Brief CV:

Robert Bird is a PDRA at Durham University, UK. He obtained his PhD in 2019 from Durham University researching hp-adaptive finite element methods for accurate crack propagation.  After his PhD he accepted a PDRA position at Imperial College London. At Imperial he developed methods to model, and quantitatively define, fracture intensity from subsurface blast shock waves in rocks. He also developed analytical methods to analyse the reflection of pulse-waves impinging on fractures. Currently at Durham he uses the material point method (MPM) for modelling rigid bodies interacting with non-linear materials.  Much of this work is focused on formulations for frictional contact and imposition of boundary conditions due to the lack of defined material boundary with the MPM. His other focus is on crack propagation, both discrete and phase-field type fracture, combined with residual based a posteriori error estimation for hp-adaptivity with the discontinuous Galerkin finite element method. The key aim with this research is to allow computational trackable simulations with no a priori knowledge of where cracks will propagate.

During Robert’s PhD he won two prizes for his distinguished research, the 2016 ACME Conference Award for Best Post-Graduate Research Student and the 2020 UKACM Roger Owen Award for the best PhD thesis. Additionally, he was a finalist in 2021 for the international ECCOMAS best PhD thesis and the 11th ECCOMAS PhD Olympiad.