Staff profile

Will Coombs is a Professor of Computational Mechanics in the Department of Engineering. He graduated with a first class MEng honors degree in Civil Engineering from Durham University in 2008. Following his undergraduate studies, Will began a PhD at Durham University within the School of Engineering and Computing Sciences, which he completed in 2011. The research conducted during this time concentrated on the theoretical development and numerical implementation of finite deformation constitutive models for pressure-sensitive particulate geomaterials. In 2011 he started as a Lecturer in School of Engineering and Computing Sciences at Durham University, he was promoted to a Senior Lecturer in 2015, Associate Professor in 2017 and Full Professor in 2021.   

Research

Will's core research interests focus on: (i) material (or constitutive) models with a specific focus on elasto-plasticity, (ii) finite-deformation mechanics, (iii) non-linear finite-elements, (iv) non-mesh-based numerical methods, (v) material point methods and (vi) fracture.  He is a member of the Department of Engineering's Computational Mechanics Research Node.  He is committed to making his research as accessible as possible, including publishing research codes in a way that is accessible to early career researchers.  One example of this is the open-source AMPLE Material Point Method (MPM) code available here.

Recently Will's research has focused on applications in offshore geotechnical engineering related to offshore wind energy, such as foundation solutions and issues related to cable installation. The adopted computational tool for these investigations is the MPM that is ideally suited to model problems involving large deformation and material failure. Durham's research group has positioned itself as a leader in implicit MPMs and has solved several issues related to application of boundary conditions, avoiding spurious issues such as volumetric locking and small cuts, and appropriate ways to formulate the MPM for different problems. 

He also develops computational tools to solve challenging problems in fracture mechanics, leveraging the capabilities of discontinuous Galerkin finite element methods to automatically adapt the finite element mesh and provide highly accurate solutions to general problems.  This has included the development of discrete fracture models using configurational force mechanics and smeared fracture representations via the phase field approach.  He is currently applying these techniques to understand ice fracture and calving processes.     

Active grants and research projects

Offshore Cable Burial: How deep is deep enough? Will leads this Engineering and Physical Sciences Research Council (EPSRC)-funded research project (grant reference EP/W000970/1) is a collaboration between Durham University, the University of Dundee and the British Geological Survey. The project focused on providing the offshore renewable energy industry with more guidance on appropriate burial depths of offshore power transmission cables to protect them for drag anchors within the Carbon Trust's Cable Burial Risk Assessment (CBRA) process.  Numerical modelling is of the highly non-linear soil-structure anchor penetration process is achieved through the Material Point Method. 

Braced Excavations: What about the corners? This Engineering and Physical Sciences Research Council (EPSRC)-funded research project (grant reference EP/X024849/1) is a collaboration between Durham University and the University of Dundee. The project is led by Professor Charles Augarde at Durham University. The aim of this project is to develop new and more accurate ways to predict ground movements and prop loads for large braced excavations as regularly used around the world for the construction of new underground transportation infrastructure. The project adopts the finite element method for the numerical analysis, and combines this with Reduced Order Models (ROMs) to explore the problem at high efficiency. 

Aura Centre for Doctoral Training (CDT) in Offshore Wind Energy. Will leads Durham's involvement in two CDTs that focus on all aspects of offshore wind energy.  Combined the programmes will train 130+ PhD students across the partner institutions, providing full funding (tuition fees and stipend) for 4 years to each student.  The CDTs are led by the University of Hull.  See here for details on the research supported by the CDT.     

Research students

Will currently supervises the following research students:

• Ted O'Hare is focused on combining non-linear micropolar continuum theory with the material point method to model large deformation strain localisation problems in geotechnical engineering. 
• Sam Sutcliffe is using the material point method to study glaciers, utilising its robustness to large deformation and power in modelling history dependent constitutive models to better capture the calving process.
• Bradley Sims is applying adaptive discontinuous Galerkin finite element phase field modelling to study fracture processes in ice, with a focus on the appropriate application of boundary conditions and loading. 
• Soheil Navvabi is developing new computational models for the optimisation of the internal structure of composite materials with a focused on offshore wind turbine blades. Funded by the Aura CDT. 
• Bayan Mohammad is researching into innovative decommissioning methods for offshore foundation systems. Funded by the Aura CDT. 
• Pranavkumar Shivakumar is using XRCT imaging and discrete element modelling to understand the role of fabric anisotropy on cyclic loading of offshore soils. Funded by the Aura CDT. 

Will is accepting new PhD students linked to his research interests and background.  

Teaching

Will is on Research Leave for the 2024/25 academic year, which means he is not delivering any taught courses during this period. Over the last five years he has delivered courses in the following areas: finite-element method, non-linear mechanics (large deformation mechanics and plasticity), contact mechanics and aircraft structures. In the past he has also taught courses on plasticity for metal forming, structural analysis, land surveying and Critical State soil mechanics as well as coursework in the areas of finite-element analysis, plasticity, contact and geometric non-linearity. 

• elasto-plasticity
• finite deformation mechanics
• finite-elements (continuous and discontinuous Galerkin)
• fracture prediction
• geomaterials
• hyperplasticity
• material point method
• stress integration
• offshore geotechnics

Chapter in book

• Sołowski, W., Berzins, M., Coombs, W., Guilkey, J., Moller, M., Tran, Q., Adibaskoro, T., Seyedan, S., Tielen, R., & Soga, K. (2021). Material point method: Overview and challenges ahead. In S. Bordas, & D. S. Balint (Eds.), Advances in Applied Mechanics (113-204). Elsevier. https://doi.org/10.1016/bs.aams.2020.12.002

Conference Paper

• Gavin, N., Coombs, W., Brigham, J., & Augarde, C. (2022, April). MRI to MPM: Developing a Patient-specific Material Point Method Model of the Human Heart. Paper presented at UKACM 2022, Nottingham, UK
• Charlton, T., Coombs, W., & Augarde, C. (2016, December). Gradient elasticity with the material point method. Presented at VII European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2016, Crete, Greece
• Pretti, G., Coombs, W., Augarde, C., Puigvert, M., Gutierrez, J., & Cross, L. (2022, August). A review of drag anchor penetration models to inform cable burial risk assessment. Paper presented at 4th International Symposium on Frontiers in Offshore Geotechnics (ISFOG), Austin, Texas
• Ghaffari Motlagh, Y., & Coombs, W. (2016, December). An implicit time integration high-order material point method for small and large deformation problems: formulation and analysis within the isogeometric framework. Presented at VII European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2016, Crete, Greece
• Pretti, G., Coombs, W., & Augarde, C. (2022, April). A comparison of approaches for modelling poro-mechanics in the Material Point Method. Paper presented at UKACM 2022, Nottingham, UK
• O'Hare, T. J., Gourgiotis, P. A., Coombs, W. M., & Augarde, C. E. (2023, April). A geometrically-exact Finite Element Method for micropolar continua with finite deformations. Paper presented at UKACM 2023, University of Warwick, Coventry, UK
• Bird, R., Pretti, G., Coombs, W. M., Augarde, C. E., Sharif, Y., Brown, M., Carter, G., & Johnson, K. (2023, April). Cone penetration tests (CPTs) in bi-phase soils: A material point approach with rigid body interaction. Paper presented at UK Association for Computational Mechanics 2023 (UKACM 2023), University of Warwick, UK
• Pretti, G., Coombs, W. M., & Augarde, C. E. (2024). Consequences of Terzaghi’s effective stress decomposition in the context of finite strain poro-mechanics. In W. M. Coombs (Ed.), UKACM Proceedings 2024 (109-112). https://doi.org/10.62512/conf.ukacm2024.019
• Bird, R., Pretti, G., Coombs, W., Augarde, C., Sharif, Y., Brown, M., …Johnson, K. (2024). Dynamic three-dimensional rigid body interaction with highly deformable solids, a material point approach. In W. Coombs (Ed.), Proceedings of the 2024 UK Association for Computational Mechanics Conference (153-156). https://doi.org/10.62512/conf.ukacm2024.092
• Sutcliffe, S. J. V., Coombs, W. M., Zhang, W., & Duddu, R. (2024). Modelling post-failure behaviour of chalk cliffs with the Material Point Method. In W. M. Coombs (Ed.), UKACM Proceedings 2024 (136-139). https://doi.org/10.62512/conf.ukacm2024.048
• O'Hare, T. J., Gourgiotis, P. A., Coombs, W. M., & Augarde, C. E. (2024). Simulation of strain localisation with an elastoplastic micropolar material point method. In W. M. Coombs (Ed.), UKACM Proceedings 2024 (141-144). https://doi.org/10.62512/conf.ukacm2024.009
• Sims, B., Bird, R. E., Coombs, W. M., & Giani, S. (2024). Immersed traction boundary conditions in phase field fracture modelling. In W. M. Coombs (Ed.), UKACM Proceedings 2024 (201-204). https://doi.org/10.62512/conf.ukacm2024.045
• Sharif, Y. U., Brown, M. J., Coombs, W. M., Augarde, C. E., Bird, R. E., Carter, G., Macdonald, C., & Johnson, K. R. (2023, September). Characterisation of anchor penetration behaviour for Cable burial risk assessment. Presented at 9th Int. SUT OSIG Conference “Innovative Geotechnologies for Energy Transition”, London, UK
• Gavin, N., Bird, R. E., Coombs, W. M., & Augarde, C. E. (2023, June). An open-source Julia code for geotechnical MPM. Presented at 10th European Conference on Numerical Methods in Geotechnical Engineering, London
• Macdonald, C., Carter, G. D. O., Johnson, K. R., Augarde, C. E., Coombs, W. M., Bird, R. E., Brown, M. J., & Sharif, Y. U. (2023, September). Depth of lowering and layered soils; a case study from across the North Sea. Paper presented at 9th Int. SUT OSIG Conference “Innovative Geotechnologies for Energy Transition”, London, UK
• Coombs, W. (2023, June). A ghost-stabilised material point method for large deformation geotechnical analysis. Presented at 10th European Conference on Numerical Methods in Geotechnical Engineering, London
• Bird, R., Coombs, W., Augarde, C., Brown, M., Sharif, Y., Carter, G., Johnson, K., & Macdonald, C. (2023, June). Cone Penetration Tests (CPTs) in layered soils: a Material Point approach. Presented at 10th European Conference on Numerical Methods in Geotechnical Engineering, London
• Sims, B., Bird, R., Giani, S., & Coombs, W. (2023, April). An investigation into the methods for modelling pre-existing cracks in phase field problems. Presented at UKACM 2023, Warwick, UK
• Gavin, N., Coombs, W., Brigham, J., & Augarde, C. (2023, April). On the development of a material point method compatible arc length solver for large deformation solid mechanics. Presented at UKACM 2023, Coventry, UK
• Coombs, W., Wang, L., & Augarde, C. (2021, May). Overcoming Volumetric Locking in Three-Dimensional Material Point Analysis. Presented at IACMAG 2021
• Coombs, W., Augarde, C., Bing, Y., Charlton, T., Cortis, M., Ghaffari Motlagh, Y., & Wang, L. (2019, December). AMPLE: A Material Point Learning Environment. Paper presented at Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, Cambridge, UK
• Coombs, W., Augarde, C., Brennan, A., Brown, M., Charlton, T., Knappett, J., Ghaffari Motlagh, Y., & Wang, L. (2019, December). On the issues associated with applying traditional Lagrangian mechanics to the material point method. Presented at Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, Cambridge, United Kingdom
• Wang, L., Cortis, M., Coombs, W., Augarde, C., Brown, M., Knappett, J., Brennan, A., Davidson, C., Richards, D., & Blake, A. (2019, December). On Implementation Aspects of Implicit MPM for 3D Analysis. Presented at Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, Cambridge, United Kingdom
• Matsui, H., Robinson, S., Brown, M., Brennan, A., Cortis, M., Coombs, W., & Augarde, C. (2019, December). Investigation into the effect of plough share leading geometry angle on cable plough performance. Presented at 16th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering (16 ARC), Taipei, Taiwan
• Wang, L., Coombs, W., & Augarde, C. (2018, July). On the Use of Advanced Material Point Methods for Problems Involving Large Rotational Deformation. Paper presented at 13th World Congress on Computational Mechanics / 2nd Pan American Congress on Computational Mechanics (WCCM 2018), New York, USA
• Davidson, C., Al-Baghdadi, T., Brown, M., Knappett, J., Brennan, A., Augarde, C., Wang, L., Coombs, W., Richards, D., Blake, A., & Ball, J. (2018, July). Centrifuge modelling of screw piles for offshore wind energy foundations. Presented at 9th International Conference on Physical Modelling in Geotechnics (ICPMG 2018), London, UK
• Wang, L., Coombs, W. M., Augarde, C. E., Brown, M. J., Knappett, J., Brennan, A., Davidson, C., Richards, D., & Blake, A. (2018, June). On the use of the material point method to model problems involving large rotational deformation. Presented at NUMGE 2018: 9th European Conference on Numerical Methods in Geotechnical Engineering, Porto, Portugal
• Coombs, W., & Ghaffari Motlagh, Y. (2018, June). On the use of NURBS plasticity for geomaterials. Presented at NUMGE 2018: 9th European Conference on Numerical Methods in Geotechnical Engineering., Porto, Portugal
• Augarde, C., Bing, Y., Charlton, T., Coombs, W., Cortis, M., Brown, M., & Brennan, A. (2018, June). Issues with the Material Point Method for geotechnical modelling, and how to address them. Presented at NUMGE 2018: 9th European Conference on Numerical Methods in Geotechnical Engineering, Porto, Portugal
• Wang, L., Coombs, W., & Augarde, C. (2018, June). On the use of advanced material point methods for problems involving large rotational deformation. Paper presented at 6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics, Glasgow, UK
• Davidson, C., Al-Baghdadi, T., Brown, M., Knappett, J., Brennan, A., Augarde, C., Coombs, W., Wang, L., Richards, D., Blake, A., & Ball, J. (2018, June). A modified CPT based installation torque prediction for large screw piles in sand. Presented at Cone Penetration Testing 2018, Delft, Netherlands
• Hashim, A., Coombs, W., Hattori, G., & Augarde, C. (2018, September). Comparison of implicit and explicit methods for non-ordinary state-based peridynamics for quasi-static problems. Presented at 28th International Workshop on Computational Mechanics of Materials (IWCMM28), Glasgow, UK
• Al-Baghdadi, T., Brown, M., Davidson, C., Knappett, J., Brennan, A., Wang, L., Coombs, W., Augarde, C., Richards, D., & Blake, A. (2017, September). CPT-based design procedure for installation torque prediction for screw piles installed in sand. Presented at 8th International Conference on Offshore Site Investigation & Geotechnics (SUT OSIG), London
• Robinson, S., Brown, M., Brennan, A., Cortis, M., Augarde, C., & Coombs, W. (2017, September). Improvement of seabed cable plough tow force prediction models. Presented at 8th International Conference on Offshore Site Investigation & Geotechnics (SUT OSIG), London, England
• Coombs, W. (2017, September). Hardening and non-associated flow NURBS plasticity. Presented at COMPLAS 2017: XIV International Conference on Computational Plasticity: Fundamentals and Applications., Barcelona, Spain
• Mukwiri, R., Ghaffari Motlagh, Y., Coombs, W., & Augarde, C. (2017, April). Energy dissipation in granular materials in triaxial tests. Presented at 25th Conference on Computational Mechanics UKACM 2017., Birmingham, UK
• Wang, L., Coombs, W., Augarde, C., & Brown, M. (2017, April). Implicit MPM with second-order convected particle domain interpolation. Presented at 25th Conference on Computational Mechanics UKACM 2017., Birmingham, UK
• Hashim, N., Coombs, W., Hattori, G., & Augarde, C. (2017, April). An implicit implementation of non-ordinary state-based peridynamics. Presented at 25th Conference on Computational Mechanics UKACM 2017., Birmingham, UK
• Adams, T., Giani, S., & Coombs, W. (2017, April). Level set based topology optimisation using high-order reinitialisation methods and the discontinuous Galerkin method. Presented at 25th Conference on Computational Mechanics UKACM 2017., Birmingham, UK
• Cortis, M., Coombs, W. M., Augarde, C. E., Robinson, S., Brennan, A., & Brown, M. (2017, April). The modelling of soil-tool interaction using the material point method. Presented at 25th Conference on Computational Mechanics UKACM 2017., Birmingham, UK
• Charlton, T. J., Coombs, W. M., & Augarde, C. E. (2017, April). On the implementation of gradient plasticity with the material point method. Presented at 25th Conference on Computational Mechanics UKACM 2017., Birmingham, UK
• Wang, L., Coombs, W., Augarde, C., Brown, M., Knappett, J., Brennan, A., Richards, D., & Blake, A. Modelling screwpile installation using the MPM. Presented at 1st International Conference on the Material Point Method (MPM 2017), Delft, Netherlands
• Charlton, T., Coombs, W., & Augarde, C. Gradient elasto-plasticity with the generalised interpolation material point method. Presented at 1st International Conference on the Material Point Method (MPM 2017), Delft, Netherlands
• Ghaffari Motlagh, Y., & Coombs, W. An implicit high-order material point method. Presented at 1st International Conference on the Material Point Method (MPM 2017), Delft, Netherlands
• Cortis, M., Coombs, W., Augarde, C., Robinson, S., Brown, M., & Brennan, A. (2017, January). Modelling seabed ploughing using the material point method. Presented at 1st International Conference on the Material Point Method (MPM 2017), Delft, Netherlands
• Bird, R., Coombs, W., & Giani, S. (2017, December). A discontinuous Galerkin hp-adaptive finite element method for brittlecrack propagation. Presented at 25th UKACM Conference on Computational Mechanics, Birmingham, UK
• Bing, Y., Cortis, M., Charlton, T., Coombs, W., & Augarde, C. (2017, December). Boundary representation and boundary condition imposition in the material point method. Presented at 25th UKACM Conference on Computational Mechanics, Birmingham, UK
• Fan, L., Augarde, C. E., & Coombs, W. M. (2017, December). The point collocation method with a local maximum entropy approach. Presented at 25th UKACM Conference on Computational Mechanics, Birmingham, UK
• Robinson, S., Brown, M., Brennan, A., Cortis, M., Augarde, C., & Coombs, W. (2016, October). Improving seabed cable plough performance for offshore renewable energy. Presented at 2nd International Conference on Renewable Energies Offshore, Lisbon, Spain
• Coombs, W. (2016, April). On the use of Plastic Inserts in Prestressed Railway Components. Presented at Railways 2016 - The Third International Conference on Railway Technology: Research, Development and Maintenance., Cagliari, Sardinia, Italy
• Charlton, T., Coombs, W., & Augarde, C. (2023, March). Gradient elasticity with the material point method. Presented at ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK
• 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
• Mukwiri, R., Ghaffari Motlagh, Y., Coombs, W., & Augarde, C. (2023, March). Energy dissipation in granular material under 1D compression. Presented at ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK
• Adams, T., Giani, S., & Coombs, W. (2023, March). Topology optimisation using level set methods and the discontinuous Galerkin method. Presented at ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK
• Ghaffari Motlagh, Y., & Coombs, W. (2023, March). A high-order material point method. Presented at ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK
• Cortis, M., Coombs, W., & Augarde, C. (2023, March). Implicit essential boundaries in the Material Point Method. Presented at 24th UK Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK
• Robinson, S., Brown, M. J., Brennan, A. J., Cortis, M., Augarde, C. E., & Coombs, W. M. (2016, December). Development of low cost 3D soil surface scanning for physical modelling. Presented at 3rd European Conference on Physical Modelling in Geotechnics (Eurofuge 2016),, Nantes, France
• Coombs, W. (2015, September). On isogeometric yield envelopes. Presented at COMPLAS 2015: XIII International Conference on Computational Plasticity: Fundamentals and Applications., Barcelona, Spain
• Charlton, T. J., Coombs, W. M., & Augarde, C. E. (2015, April). On the implicit implementation of the Generalised Interpolation Material Point method. Presented at 23rd Conference of the Association for Computational Mechanics in Engineering, ACME-UK 2015., Swansea, Wales, UK
• Coombs, W., & Crouch, R. (2014, August). Fabric anisotropy & DEM informed two-surface hyperplasticity: constitutive formulation, asymptotic states & experimental validation. Presented at TC105 ISSMGE international symposium on Geomechanics from Micro to Macro, Cambridge, UK
• Charlton, T., Coombs, W., & Augarde, C. (2014, April). A review of the Material Point Method and its links to other computational methods. Presented at 22nd UK National Conference of the Association of Computational Mechanics in Engineering (ACME)., Exeter, Uk
• Coombs, W. (2013, September). Unique Critical State single-surface anisotropic hyperplasticity. Presented at XII International Conference on Computational Plasticity. Fundamentals and Applications. COMPLAS XII, Barcelona, Spain
• Ullah, Z., Augarde, C. E., & Coombs, W. M. (2013, March). Three-dimensional FE-EFGM adaptive coupling with application to nonlinear adaptive analysis. Presented at International Conference on Computational Mechanics (CM13), Durham University, Durham, UK
• Ullah, Z., Augarde, C., & Coombs, W. (2013, December). Three-dimensional FE-EFGM adaptive coupling and its applications in the nonlinear adaptive analysis. Presented at CM13, Durham, UK
• Coombs, W., Crouch, R., & Heaney, C. (2012, March). Plane-strain Mohr-Coulomb inelasticity. Presented at 20th UK National Conference of the Association for Computational Mechanics in Engineering (ACME), Manchester, UK
• Ullah, Z., Augarde, C. E., & Coombs, W. M. (2012, March). Adaptive modelling of finite strain shear band localization using the element-free Galerkin method. Presented at 20th UK Conference of the Association for Computational Mechanics in Engineering (ACME), University of Manchester, Manchester, UK
• Coombs, W., & Crouch, R. (2011, September). Reuleaux plasticity: improving Mohr-Coulomb and Drucker-Prager. Presented at Geotechnical Engineering: New Horizons. Proceedings of the 21st European Young Geotechnical Engineers' Conference, Rotterdam, the Netherlands
• Coombs, W. M., Crouch, R. S., & Augarde, C. E. (2011, July). On the f fields of inadmissible stress space. Presented at Computational Plasticity XI: Fundamentals and Applications (COMPLAS XI)., Barcelona, Spain
• Coombs, W. M., Crouch, R. S., & Augarde, C. E. (2011, April). Unique Critical State Hyperplasticity. Presented at Proceedings of the 19th UK National Conference of the Association for Computational Mechanics in Engineering, Heriot-Watt University, Edinburgh
• Ullah, Z., Augarde, C. E., Crouch, R. S., & Coombs, W. M. (2011, April). FE-EFGM Coupling using maximum entropy shape functions and its application to small and finite deformation. Presented at 19th UK Conference of the Association for Computational Mechanics in Engineering (ACME), Heriot-Watt University, Edinburgh, UK
• Coombs, W., Crouch, R., & Augarde, C. (2010, June). 70-line 3D finite deformation elastoplastic finite-element code. Presented at 7th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE), Trondheim, Norway
• Heaney, C., Augarde, C., Deeks, A., Coombs, W., & Crouch, R. (2010, June). Advances in meshless methods with application to geotechnics. Presented at 7th European Conference on Numerical Methods in Geotechnical Engineering, Trondheim, Norway
• Coombs, W. M., Crouch, R. S., & Augarde, C. E. (2010, April). On the use of Reuleaux plasticity for geometric non-linear analysis. Presented at 18th UK Conference on Computational Mechanics (ACME), Southampton, England
• Coombs, W., Crouch, R., & Augarde, C. (2009, September). Influence of Lode Angle Dependency on the Critical State for Rotational Plasticity. Presented at Computational Plasticity X: Fundamentals and Applications (COMPLAS X), Barcelona, Spain
• Coombs, W., Crouch, R., & Augarde, C. (2009, December). On the necessity for rotational yielding in anisotropic plasticity. Presented at 17th UK Conference on Computational Mechanics (ACME), Nottingham, England

Conference Proceeding

• (2024, April). UKACM Proceedings 2024. Presented at 2024 UK Association for Computational Mechanics Conference, Durham, UK

Doctoral Thesis

• Coombs, W. (2011). Finite deformation of particulate geomaterials: frictional and anisotropic Critical State elasto-plasticity. (Thesis). School of Engineering and Computing Sciences, Durham University. https://durham-repository.worktribe.com/output/1642168

Edited book

• Toll, D., Zhu, H., Osman, A., Coombs, W., Li, X., & Rouainia, M. (Eds.). (2014). Information Technology in Geo-Engineering. IOS Press

Journal Article

• Pretti, G., Bird, R., Gavin, N., Coombs, W., & Augarde, C. (in press). A stable poro-mechanical formulation for Material Point Methods leveraging overlapping meshes and multi-field ghost penalisation. International Journal for Numerical Methods in Engineering,
• Sharif, Y., Brown, M. J., Knappett, J., Davidson, C., Bird, R., Coombs, W., Augarde, C., Carter, G., Macdonald, C., & Johnson, K. (in press). Comparison of 1g and centrifuge modelling of drag embedment anchors with subsurface wireless tracking. International Journal of Physical Modelling in Geotechnics,
• 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
• Gavin, N., Pretti, G., Coombs, W., Brigham, J., & Augarde, C. (2024). On the implementation of a material point‐based arc‐length method. International Journal for Numerical Methods in Engineering, 125(9), Article e7438. https://doi.org/10.1002/nme.7438
• Pretti, G., Coombs, W., Augarde, C., Marchena Puigvert, M., & Reyna Gutierrez, J. A. (2024). Preserving non-negative porosity values in a bi-phase elasto-plastic material under Terzaghi’s effective stress principle. Mechanics of Materials, 192, Article 104958. https://doi.org/10.1016/j.mechmat.2024.104958
• O'Hare, T., Gourgiotis, P., Coombs, W., & Augarde, C. (2024). An implicit Material Point Method for micropolar solids undergoing large deformations. Computer Methods in Applied Mechanics and Engineering, 419, Article 116668. https://doi.org/10.1016/j.cma.2023.116668
• Coombs, W. (2023). Ghost stabilisation of the Material Point Method for stable quasi-static and dynamic analysis of large deformation problems. International Journal for Numerical Methods in Engineering, 124(21), 4841-4875. https://doi.org/10.1002/nme.7332
• 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
• Chihadeh, A., Coombs, W., & Kaliske, M. (2023). A coupled implicit MPM-FEM approach for brittle fracture and fragmentation. Computers and Structures, 288, Article 107143. https://doi.org/10.1016/j.compstruc.2023.107143
• Pretti, G., Coombs, W., Augarde, C., Sims, B., Puigvert, M., & Gutierrez, J. (2023). A conservation law consistent updated Lagrangian material point method for dynamic analysis. Journal of Computational Physics, 485, Article 112075. https://doi.org/10.1016/j.jcp.2023.112075
• Bird, R., Coombs, W., & Giani, S. (2022). Adaptive Configurational Force-based crack propagation for brittle and fatigue analysis. International Journal for Numerical Methods in Engineering, 123(7), 1673-1709. https://doi.org/10.1002/nme.6911
• Davidson, C., Brown, M., Cerfontaine, B., Knappett, J., Brennan, A., Al-Baghdadi, T., Augarde, C., Coombs, W., Wang, L., Blake, A., Richards, D., & Ball, J. (2022). Physical modelling to demonstrate the feasibility of screw piles for offshore jacket supported wind energy structures. Géotechnique, 72(2), 108-126. https://doi.org/10.1680/jgeot.18.p.311
• Zhou, R., Coombs, W., Xu, Y., Zhang, P., & Wang, L.-G. (2022). A configurational force-based material point method for crack propagation modelling in 2D  . Theoretical and Applied Fracture Mechanics, 117, Article 103186. https://doi.org/10.1016/j.tafmec.2021.103186
• 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
• Pretti, G., Coombs, W., & Augarde, C. (2022). A Displacement-controlled Arc-Length Solution Scheme. Computers and Structures, 258, Article 106674. https://doi.org/10.1016/j.compstruc.2021.106674
• Golchin, A., Vardon, P., Hicks, M., & Coombs, W. (2021). A flexible and robust yield function for geomaterials. Computer Methods in Applied Mechanics and Engineering, 387, Article 114162. https://doi.org/10.1016/j.cma.2021.114162
• Fan, L., Coombs, W., & Augarde, C. (2021). An adaptive local maximum entropy point collocation method for linear elasticity  . Computers and Structures, 256, Article 106644. https://doi.org/10.1016/j.compstruc.2021.106644
• Robinson, S., Brown, M., Matsui, H., Brennan, A., Augarde, C., Coombs, W., & Cortis, M. (2021). A cone penetration test (CPT) approach to cable plough performance prediction based upon centrifuge model testing. Canadian Geotechnical Journal, 58(10), 1466-1477. https://doi.org/10.1139/cgj-2020-0366
• Sharif, Y., Brown, M., Cerfontaine, B., Davidson, C., Ciantia, M., Knappett, J., Brennan, A., Ball, J., Augarde, C., Coombs, W., Blake, A., Richards, D., White, D., Huisman, M., & Ottolini, M. (2021). Effects of screw pile installation on installation requirements and in-service performance using the Discrete Element Method. Canadian Geotechnical Journal, 58(9), 1334-1350. https://doi.org/10.1139/cgj-2020-0241
• Wang, L., Coombs, W., Augarde, C., Cortis, M., Brown, M., Brennan, A., Knappett, J., Davidson, C., Richards, D., White, D., & White, A. (2021). An efficient and locking-free material point method for three dimensional analysis with simplex elements. International Journal for Numerical Methods in Engineering, 122(15), 3876-3899. https://doi.org/10.1002/nme.6685
• Cerfontaine, B., Knappett, J., Brown, M., Davidson, C., Al-Baghdadi, T., Sharif, Y., Brennan, A., Augarde, C., Coombs, W., Wang, L., Blake, A., Richards, D., & Ball, J. (2021). A Finite Element approach for determining the full load-displacement relationship of axially-loaded shallow screw anchors, incorporating installation effects. Canadian Geotechnical Journal, 58(4), 565-582. https://doi.org/10.1139/cgj-2019-0548
• Hashim, N. A., Coombs, W., Augarde, C., & Hattori, G. (2020). An implicit non-ordinary state-based peridynamics with stabilised correspondence material model for finite deformation analysis. Computer Methods in Applied Mechanics and Engineering, 371, Article 113304. https://doi.org/10.1016/j.cma.2020.113304
• Nguyen, K., Augarde, C., Coombs, W., Nguyen-Xuan, H., & Abdel-Wahab, M. (2020). Non-conforming multipatches for NURBS-based finite element analysis of higher-order phase-field models for brittle fracture. Engineering Fracture Mechanics, 235, Article 107133. https://doi.org/10.1016/j.engfracmech.2020.107133
• Coombs, W., Augarde, C., Brennan, A., Brown, M., Charlton, T., Knappett, J., Ghaffari Motlagh, Y., & Wang, L. (2020). On Lagrangian mechanics and the implicit material point method for large deformation elasto-plasticity. Computer Methods in Applied Mechanics and Engineering, 358, Article 112622. https://doi.org/10.1016/j.cma.2019.112622
• Lu, K., Coombs, W., Augarde, C., & Hu, L. (2020). An implicit boundary finite element method with extension to frictional sliding boundary conditions and elasto-plastic analyses. Computer Methods in Applied Mechanics and Engineering, 358, Article 112620. https://doi.org/10.1016/j.cma.2019.112620
• Coombs, W., & Augarde, C. (2020). AMPLE: A Material Point Learning Environment. Advances in Engineering Software, 139, Article 102748. https://doi.org/10.1016/j.advengsoft.2019.102748
• Robinson, S., Brown, M., Matsui, H., Brennan, A., Augarde, C., Coombs, W., & Cortis, M. (2019). Centrifuge testing to verify scaling of offshore pipeline ploughs. International Journal of Physical Modelling in Geotechnics, 19(6), 305-317. https://doi.org/10.1680/jphmg.17.00075
• Adams, T., McLeish, N., Giani, S., & Coombs, W. (2019). A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation. Computers and Mathematics with Applications, 78(9), 2944-2960. https://doi.org/10.1016/j.camwa.2019.01.032
• Wang, L., Coombs, W., Augarde, C., Cortis, M., Charlton, T., Brown, M., Knappett, J., Brennan, A., Davidson, C., Richards, D., & Blake, A. (2019). On the use of domain-based material point methods for problems involving large distortion. Computer Methods in Applied Mechanics and Engineering, 355, 1003-1025. https://doi.org/10.1016/j.cma.2019.07.011
• 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
• 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
• Lu, K., Augarde, C., Coombs, W., & Hu, Z. (2019). Weak impositions of Dirichlet boundary conditions in solid mechanics: a critique of current approaches and extension to partially prescribed boundaries. Computer Methods in Applied Mechanics and Engineering, 348, 632-659. https://doi.org/10.1016/j.cma.2019.01.035
• 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
• Bing, Y., Cortis, M., Charlton, T., Coombs, W., & Augarde, C. (2019). B-spline based boundary conditions in the material point method. Computers and Structures, 212, 257-274. https://doi.org/10.1016/j.compstruc.2018.11.003
• Adams, T., Giani, S., & Coombs, W. (2019). A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation. Journal of Computational Physics, 379, 373-391. https://doi.org/10.1016/j.jcp.2018.12.003
• 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
• Hattori, G., Trevelyan, J., & Coombs, W. (2018). A non-ordinary state-based peridynamics framework for anisotropic materials. Computer Methods in Applied Mechanics and Engineering, 339, 416-442. https://doi.org/10.1016/j.cma.2018.05.007
• Coombs, W., & Ghaffari Motlagh, Y. (2018). NURBS plasticity: non-associated plastic flow. Computer Methods in Applied Mechanics and Engineering, 336, 419-443. https://doi.org/10.1016/j.cma.2018.03.015
• Fan, L., Coombs, W., & Augarde, C. (2018). The point collocation method with a local maximum entropy approach. Computers and Structures, 201, 1-14. https://doi.org/10.1016/j.compstruc.2018.02.008
• Coombs, W., Charlton, T., Cortis, M., & Augarde, C. (2018). Overcoming volumetric locking in material point methods. Computer Methods in Applied Mechanics and Engineering, 333, 1-21. https://doi.org/10.1016/j.cma.2018.01.010
• 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
• Cortis, M., Coombs, W., Augarde, C., Brown, M., Brennan, A., & Robinson, S. (2018). Imposition of essential boundary conditions in the material point method. International Journal for Numerical Methods in Engineering, 113(1), 130-152. https://doi.org/10.1002/nme.5606
• 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
• Charlton, T., Coombs, W., & Augarde, C. (2017). iGIMP: An implicit generalised interpolation material point method for large deformations. Computers and Structures, 190, 108-125. https://doi.org/10.1016/j.compstruc.2017.05.004
• Coombs, W., & Ghaffari Motlagh, Y. (2017). NURBS plasticity: yield surface evolution and implicit stress integration for isotropic hardening. Computer Methods in Applied Mechanics and Engineering, 324, 204-220. https://doi.org/10.1016/j.cma.2017.05.017
• Hattori, G., Trevelyan, J., Augarde, C., Coombs, W., & Aplin, A. (2017). Numerical simulation of fracking in shale rocks: current state and future approaches. Archives of Computational Methods in Engineering, 24(2), 281-317. https://doi.org/10.1007/s11831-016-9169-0
• Coombs, W. (2017). Continuously unique anisotropic Critical State hyperplasticity. International Journal for Numerical and Analytical Methods in Geomechanics, 41(4), 578-601. https://doi.org/10.1002/nag.2571
• Ullah, Z., Coombs, W. M., & Augarde, C. E. (2016). Parallel computations in nonlinear solid mechanics using adaptive finite element and meshless methods. Engineering Computations, 33(4), 1161-1191. https://doi.org/10.1108/EC-06-2015-0166
• Coombs, W., Petit, O., & Ghaffari Motlagh, Y. (2016). NURBS plasticity: yield surface representation and implicit stress integration for isotropic inelasticity. Computer Methods in Applied Mechanics and Engineering, 304, 342-358. https://doi.org/10.1016/j.cma.2016.02.025
• Cowan, T., & Coombs, W. (2014). Rotationally invariant distortion resistant finite-elements. Computer Methods in Applied Mechanics and Engineering, 275, 189-203. https://doi.org/10.1016/j.cma.2014.02.016
• Ullah, Z., Coombs, W. M., & Augarde, C. E. (2013). An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems. Computer Methods in Applied Mechanics and Engineering, 267, 111-132. https://doi.org/10.1016/j.cma.2013.07.018
• Coombs, W., Crouch, R., & Heaney, C. (2013). Observations on Mohr-Coulomb plasticity under plane strain. Journal of Engineering Mechanics, 139(9), 1218-1228. https://doi.org/10.1061/%28asce%29em.1943-7889.0000568
• Coombs, W., Crouch, R., & Augarde, C. (2013). A unique Critical State two-surface hyperplasticity model for fine-grained particulate media. Journal of the Mechanics and Physics of Solids, 61(1), 175-189. https://doi.org/10.1016/j.jmps.2012.08.002
• Coombs, W., & Crouch, R. (2011). Non-associated Reuleaux plasticity: analytical stress integration and consistent tangent for finite deformation mechanics. Computer Methods in Applied Mechanics and Engineering, 200(9-12), 1021-1037. https://doi.org/10.1016/j.cma.2010.11.012
• Coombs, W., & Crouch, R. (2011). Algorithmic issues for three-invariant hyperplastic Critical State models. Computer Methods in Applied Mechanics and Engineering, 200(25-28), 2297-2318. https://doi.org/10.1016/j.cma.2011.03.019
• Coombs, W., Crouch, R., & Augarde, C. (2010). Reuleaux plasticity: analytical backward Euler stress integration and consistent tangent. Computer Methods in Applied Mechanics and Engineering, 199(25-28), 1733-1743. https://doi.org/10.1016/j.cma.2010.01.017

Other (Print)

• Coombs, W. (2024, September). Stability of implicit material point methods for geotechnical analysis of large deformation problems. Presented at ALERT Geomaterials 2024, Aussois, France
• Coombs, W., & Ghaffari Motlagh, Y. (2017). Resilience of rail support systems: the use of plastic sockets
• Coombs, W., & Ghaffari Motlagh, J. (2015). Resilience of Concrete Rail Support Systems

Report

• Johnson, K. R., Carter, G., & Macdonald, C. (2024). Layered soils in the shallow subsurface (
• Ullah, Z., Augarde, C. E., & Coombs, W. M. (2013). Local maximum entropy shape functions based FE-EFGM coupling. [No known commissioning body]