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Accurate Configuration Force Evaluation via hp-adaptive Discontinuous Galerkin Finite Element Analysis (2019)
Journal Article
Bird, R., Coombs, W., & Giani, S. (2019). Accurate Configuration Force Evaluation via hp-adaptive Discontinuous Galerkin Finite Element Analysis. Engineering Fracture Mechanics, 216, Article 106370. https://doi.org/10.1016/j.engfracmech.2019.02.029

Engineers require accurate determination of the configurational force at the crack tip, and corresponding stress intensity factors, for fracture fatigue analysis and accurate crack propagation. However, obtaining highly accurate crack tip configurati... Read More about Accurate Configuration Force Evaluation via hp-adaptive Discontinuous Galerkin Finite Element Analysis.

A configurational force driven cracking particle method for modelling crack propagation in 2D (2019)
Journal Article
Ai, W., Bird, R., Coombs, W., & Augarde, C. (2019). A configurational force driven cracking particle method for modelling crack propagation in 2D. Engineering Analysis with Boundary Elements, 104, 197-208. https://doi.org/10.1016/j.enganabound.2019.03.008

This paper presents a novel combination of two numerical techniques to produce a method for solving fracture mechanics problems. A weak form meshless method, the cracking particles method, forms the basis of the mechanical model while crack propagati... Read More about A configurational force driven cracking particle method for modelling crack propagation in 2D.

Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB (2019)
Journal Article
O'Sullivan, S., Bird, R., Coombs, W., & Giani, S. (2019). Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB. Computers and Mathematics with Applications, 78(9), 3007-3026. https://doi.org/10.1016/j.camwa.2019.03.012

MATLAB is adept at the development of concise Finite Element (FE) routines, however it is commonly perceived to be too inefficient for high fidelity analysis. This paper aims to challenge this preconception by presenting two optimised FE codes for bo... Read More about Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB.

A posteriori discontinuous Galerkin error estimator for linear elasticity (2018)
Journal Article
Bird, R., Coombs, W., & Giani, S. (2019). A posteriori discontinuous Galerkin error estimator for linear elasticity. Applied Mathematics and Computation, 344-345, 78-96. https://doi.org/10.1016/j.amc.2018.08.039

This paper presents for the first time the derivation of an hp a posteriori error estimator for the symmetric interior penalty discontinuous Galerkin finite element method for linear elastic analysis. Any combination of Neumann and Dirichlet boundary... Read More about A posteriori discontinuous Galerkin error estimator for linear elasticity.

Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults (2018)
Journal Article
Guérin‐Marthe, S., Nielsen, S., Bird, R., Giani, S., & Di Toro, G. (2018). Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults. Journal of Geophysical Research. Solid Earth, 124(1), 689-708. https://doi.org/10.1029/2018jb016803

Recent GPS observations of major earthquakes such as the 2014 Chile megathrust show a slow pre‐slip phase releasing a significant portion of the total moment (Ruiz et al., 2014). Despite advances from theoretical stability analysis (Rubin & Ampuero,... Read More about Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults.

A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials (2017)
Journal Article
Bird, R., Coombs, W., & Giani, S. (2018). A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials. International Journal for Numerical Methods in Engineering, 113(7), 1061-1080. https://doi.org/10.1002/nme.5699

This paper presents a framework for r-adaptive quasi-static configurational force (CF) brittle crack propagation, cast within a discontinuous Galerkin (DG) symmetric interior penalty (SIPG) finite element scheme. Cracks are propagated in discrete ste... Read More about A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials.

Fast native-MATLAB stiffness assembly for SIPG linear elasticity (2017)
Journal Article
Bird, R., Coombs, W., & Giani, S. (2017). Fast native-MATLAB stiffness assembly for SIPG linear elasticity. Computers and Mathematics with Applications, 74(12), 3209-3230. https://doi.org/10.1016/j.camwa.2017.08.022

When written in MATLAB the finite element method (FEM) can be implemented quickly and with significantly fewer lines, when compared to compiled code. MATLAB is also an attractive environment for generating bespoke routines for scientific computation... Read More about Fast native-MATLAB stiffness assembly for SIPG linear elasticity.

Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity (2016)
Presentation / Conference Contribution
Bird, R., Coombs, W., & Giani, S. (2023, March). Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity. Presented at ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK

This paper presents a quasi-static configurational force (CF) brittle fracture propagation method, [1], using the discontinuous Galerkin (dG) symmetric interior penalty (SIP) method, [2]. The method is derived from the first law of thermodynamics wit... Read More about Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity.