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Dr Robert Bird's Outputs (14)

The Stress-Continuous Material Point Method: a technique to alleviate cell-crossing instability while retaining linear shape functions (2025)
Journal Article
Pretti, G., Bird, R., Coombs, W., Augarde, C., & Giani, S. (in press). The Stress-Continuous Material Point Method: a technique to alleviate cell-crossing instability while retaining linear shape functions. Computer Methods in Applied Mechanics and Engineering,

The Material Point Method (MPM) for solid mechanics continues to attract much interest from those wishing to solve complex non-linear mechanics problems which include large deformations. Its prominence is rising in many areas of engineering, such as... Read More about The Stress-Continuous Material Point Method: a technique to alleviate cell-crossing instability while retaining linear shape functions.

The Aggregated Material Point Method (AgMPM) (2025)
Journal Article
Coombs, W., Bird, R., & Pretti, G. (2025). The Aggregated Material Point Method (AgMPM). Computer Methods in Applied Mechanics and Engineering, 442, Article 118012. https://doi.org/10.1016/j.cma.2025.118012

The Material Point Method (MPM) has been shown to be an effective approach for analysing large deformation processes across a range of physical problems. However, the method suffers from a number of spurious artefacts, such as a widely documented ce... Read More about The Aggregated Material Point Method (AgMPM).

A stable poro-mechanical formulation for Material Point Methods leveraging overlapping meshes and multi-field ghost penalisation (2025)
Journal Article
Pretti, G., Bird, R., Gavin, N., Coombs, W., & Augarde, C. (2025). A stable poro-mechanical formulation for Material Point Methods leveraging overlapping meshes and multi-field ghost penalisation. International Journal for Numerical Methods in Engineering, 126(5), Article e7630. https://doi.org/10.1002/nme.7630

The Material Point Method (MPM) is widely used to analyse coupled (solid-water) problems under large deformations/displacements. However, if not addressed carefully, MPM u-p formulations for poro-mechanics can be affected by two major sources of inst... Read More about A stable poro-mechanical formulation for Material Point Methods leveraging overlapping meshes and multi-field ghost penalisation.

An implicit material point-to-rigid body contact approach for large deformation soil-structure interaction (2024)
Journal Article
Bird, R., Pretti, G., Coombs, W., Augarde, C., Sharif, Y., Brown, M., Carter, G., Macdonald, C., & Johnson, K. (2024). An implicit material point-to-rigid body contact approach for large deformation soil-structure interaction. Computers and Geotechnics, 174, Article 106646. https://doi.org/10.1016/j.compgeo.2024.106646

Modelling the interaction between rigid and deformable bodies holds significant relevance in geotechnical engineering, particularly in scenarios involving stiff engineering objects interacting with highly deformable material such as soil. These proce... Read More about An implicit material point-to-rigid body contact approach for large deformation soil-structure interaction.

An hp-adaptive discontinuous Galerkin method for phase field fracture (2023)
Journal Article
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

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... Read More about An hp-adaptive discontinuous Galerkin method for phase field fracture.

An open source hp-adaptive discontinuous Galerkin finite element solver for linear elasticity (2022)
Journal Article
Wiltshire, T., Bird, R. E., Coombs, W. M., & Giani, S. (2022). An open source hp-adaptive discontinuous Galerkin finite element solver for linear elasticity. Advances in Engineering Software, 171, https://doi.org/10.1016/j.advengsoft.2022.103147

Open source codes are a key ingredient to greater research integrity and accountability in computational science and engineering. However, many of these codes have not been developed with modification of the base code as their primary consideration.... Read More about An open source hp-adaptive discontinuous Galerkin finite element solver for linear elasticity.

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.