Staff profile

Will Coombs is a Professor in Computational Mechanics in the Department of Engineering at Durham University, UK.  Will originally trained as a Civil Engineer before studying for a PhD in Computational Mechanics, focused on constitutive modelling of soils under large deformations, which he completed in 2011.  In the same year he was appointed as a Lecturer at Durham University.  Since that time, he has secured research funding exceeding £14M and published over 50 peer reviewed journal papers in areas such as: (i) constitutive modelling of soils, (ii) plasticity formulations, (iii) advanced finite element methods, (iv) imposition of boundary conditions, (v) meshless/meshfree methods, (vi) the material point method, (vii) topology optimization and (viii) computational fracture mechanics.  He is also 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 code available here.

 

Research

In more detail, Will's primary research interest surrounds inelastic constitutive modelling of geomaterials subjected to finite deformations. Included within this is the theoretical development and numerical implementation of a range of material constitutive models, from simple, rapid and robust isotropic models to complex anisotropic material behaviour frameworks. His research continues on the development on constitutive models for a variety of engineering materials, including complex particulate behaviour. One aim in this area is relating the observed material behaviour to tangible and measurable material properties and fabric constituents whilst respecting the fundamental laws of thermodynamics.

In addition to research on constitutive modelling, Will has developed a series of cutting-edge, compact and freely available Finite Element Method and Material Point Method codes for problems involving large deformation and material failure (elasto-plasticity). These codes form a lauchpad to test out research ideas, especially for research students, and provide ideal environments for new collaborations. 

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 Material Point Method (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 appropriate ways to formulate MPM equilibrium equations. 

 

Teaching

Will currently teaches 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., …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

• Toll, D., & O’Dea, J. An XML data format for geotechnical data: AGSML4. In D. G. Toll, H. Zhu, A. Osman, W. Coombs, X. Li, & M. Rouainia (Eds.),
• Ghaffari Motlagh, Y., & Coombs, W. (in press). An implicit time integration high-order material point method for small and large deformation problems: formulation and analysis within the isogeometric framework.
• Charlton, T., Coombs, W., & Augarde, C. (in press). Gradient elasticity with the material point method.
• Coombs, W. (2023). A ghost-stabilised material point method for large deformation geotechnical analysis. In L. Zdravkovic, S. Konte, D. Taborda, & A. Tsiampousi (Eds.), . https://doi.org/10.53243/numge2023-57
• Bird, R., Coombs, W., Augarde, C., Brown, M., Sharif, Y., Carter, G., …Macdonald, C. (2023). Cone Penetration Tests (CPTs) in layered soils: a Material Point approach. In L. Zdravkovic, S. Kontoe, D. . M. . G. Taborda, & A. Tsiampousi (Eds.), . https://doi.org/10.53243/numge2023-743
• Gavin, N., Bird, R. E., Coombs, W. M., & Augarde, C. E. (2023). An open-source Julia code for geotechnical MPM. In L. Zdravkovic, S. Kontoe, D. M. G. Taborda, & A. Tsiampousi (Eds.), . https://doi.org/10.53243/numge2023-35
• Sims, B., Bird, R., Giani, S., & Coombs, W. (2023). An investigation into the methods for modelling pre-existing cracks in phase field problems.
• Gavin, N., Coombs, W., Brigham, J., & Augarde, C. (2023). On the development of a material point method compatible arc length solver for large deformation solid mechanics.
• Coombs, W., Wang, L., & Augarde, C. (2021). Overcoming Volumetric Locking in Three-Dimensional Material Point Analysis. In M. Barla, A. Di Donna, & D. Sterpi (Eds.), Challenges and Innovations in Geomechanics. IACMAG 2021 (772-778). https://doi.org/10.1007/978-3-030-64514-4_82
• Matsui, H., Robinson, S., Brown, M., Brennan, A., Cortis, M., Coombs, W., & Augarde, C. (2019). Investigation into the effect of plough share leading geometry angle on cable plough performance.
• Wang, L., Cortis, M., Coombs, W., Augarde, C., Brown, M., Knappett, J., …Blake, A. (2019). On Implementation Aspects of Implicit MPM for 3D Analysis.
• Coombs, W., Augarde, C., Brennan, A., Brown, M., Charlton, T., Knappett, J., …Wang, L. (2019). On the issues associated with applying traditional Lagrangian mechanics to the material point method.
• Davidson, C., Al-Baghdadi, T., Brown, M., Knappett, J., Brennan, A., Augarde, C., …Ball, J. (2018). Centrifuge modelling of screw piles for offshore wind energy foundations. In A. McNamara, S. Divall, R. Goodey, N. Taylor, S. Stallebrass, & J. Panchal (Eds.), Physical modelling in geotechnics : proceedings of the 9th International Conference on Physical Modelling in Geotechnics (ICPMG 2018), July 17-20, 2018, London, United Kingdom. Volume 1 (695-700)
• Wang, L., Coombs, W. M., Augarde, C. E., Brown, M. J., Knappett, J., Brennan, A., …Blake, A. (2018). On the use of the material point method to model problems involving large rotational deformation. In A. S. Cardoso, J. L. Borges, P. A. Costa, A. T. Gomes, J. C. Marques, & C. S. Vieira (Eds.), Numerical Methods in Geotechnical Engineering IX, Volume 1 : Proceedings of the 9th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2018), June 25-27, 2018, Porto, Portugal (585-592)
• Augarde, C., Bing, Y., Charlton, T., Coombs, W., Cortis, M., Brown, M., & Brennan, A. (2018). Issues with the Material Point Method for geotechnical modelling, and how to address them. In A. . S. Cardoso, J. . L. Borges, P. . A. Costa, A. . T. Gomes, J. . C. Marques, & C. . S. Vieira (Eds.), Numerical Methods in Geotechnical Engineering IX, Volume 1 : Proceedings of the 9th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2018), June 25-27, 2018, Porto, Portugal (593-601)
• Coombs, W., & Ghaffari Motlagh, Y. (2018). On the use of NURBS plasticity for geomaterials. In A. S. Cardoso, J. L. Borges, P. A. Costa, A. T. Gomes, J. C. Marques, & C. S. Vieira (Eds.), Numerical Methods in Geotechnical Engineering IX, Volume 1 : Proceedings of the 9th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2018), June 25-27, 2018, Porto, Portugal (47-52)
• Davidson, C., Al-Baghdadi, T., Brown, M., Knappett, J., Brennan, A., Augarde, C., …Ball, J. (2018). A modified CPT based installation torque prediction for large screw piles in sand. In M. A. Hicks, F. Pisanò, & J. Peuchen (Eds.), Cone Penetration Testing IV 2018 : proceedings of the 4th International Symposium on Cone Penetration Testing (CPT'18), 21-22 June, 2018, Delft, The Netherlands (255-261). https://doi.org/10.1201/9780429505980
• Hashim, A., Coombs, W., Hattori, G., & Augarde, C. (2018). Comparison of implicit and explicit methods for non-ordinary state-based peridynamics for quasi-static problems.
• Al-Baghdadi, T., Brown, M., Davidson, C., Knappett, J., Brennan, A., Wang, L., …Blake, A. (2017). CPT-based design procedure for installation torque prediction for screw piles installed in sand. In Offshore site investigation and geotechnics : integrated geotechnologies - present and future : proceedings of the 8th international conference, held 12–14 September 2017 at the Royal Geographical Society, London (346-353)
• Robinson, S., Brown, M., Brennan, A., Cortis, M., Augarde, C., & Coombs, W. (2017). Improvement of seabed cable plough tow force prediction models. In Offshore site investigation and geotechnics : integrated geotechnologies - present and future. Proceedings of the 8th international conference, held 12–14 September 2017 at the Royal Geographical Society, London (914-921)
• Coombs, W. (2017). Hardening and non-associated flow NURBS plasticity. In E. Oñate, D. R. J. Owen, D. Peric, & M. Chiumenti (Eds.), Proceedings of the XIV International Conference on Computational Plasticity. Fundamentals and Applications (COMPLAS 2017), 5-7 September 2017, Barcelona, Spain (363-372)
• Charlton, T. J., Coombs, W. M., & Augarde, C. E. (2017). On the implementation of gradient plasticity with the material point method. In A. Faramarzi, & S. Dirar (Eds.), Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017) : 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK (240-243)
• Adams, T., Giani, S., & Coombs, W. (2017). Level set based topology optimisation using high-order reinitialisation methods and the discontinuous Galerkin method. In A. Faramarzi, & S. Dirar (Eds.), Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017) : 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK (18-21)
• Mukwiri, R., Ghaffari Motlagh, Y., Coombs, W., & Augarde, C. (2017). Energy dissipation in granular materials in triaxial tests. In A. Faramarzi, & S. Dirar (Eds.), Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017) : 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK (191-194)
• Wang, L., Coombs, W., Augarde, C., & Brown, M. (2017). Implicit MPM with second-order convected particle domain interpolation. In A. Faramarzi, & S. Dirar (Eds.), Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017) : 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK (264-267)
• Hashim, N., Coombs, W., Hattori, G., & Augarde, C. (2017). An implicit implementation of non-ordinary state-based peridynamics. In A. Faramarzi, & S. Dirar (Eds.), Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017) : 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK (134-137)
• Cortis, M., Coombs, W. M., Augarde, C. E., Robinson, S., Brennan, A., & Brown, M. (2017). The modelling of soil-tool interaction using the material point method. In A. Faramarzi, & S. Dirar (Eds.), Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017) : 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK (211-214)
• Charlton, T., Coombs, W., & Augarde, C. (2017). Gradient elasto-plasticity with the generalised interpolation material point method. Procedia engineering, 175, 110-115. https://doi.org/10.1016/j.proeng.2017.01.036
• Wang, L., Coombs, W., Augarde, C., Brown, M., Knappett, J., Brennan, A., …Blake, A. (2017). Modelling screwpile installation using the MPM. Procedia engineering, 175, 124-132. https://doi.org/10.1016/j.proeng.2017.01.040
• Cortis, M., Coombs, W., Augarde, C., Robinson, S., Brown, M., & Brennan, A. (2017). Modelling seabed ploughing using the material point method. In A. Rohe, K. Soga, H. Teunissen, & B. Z. Coelho (Eds.), . https://doi.org/10.1016/j.proeng.2017.01.002
• Ghaffari Motlagh, Y., & Coombs, W. (2017). An implicit high-order material point method. Procedia engineering, 175, 8-13. https://doi.org/10.1016/j.proeng.2017.01.003
• Bing, Y., Cortis, M., Charlton, T., Coombs, W., & Augarde, C. (2017). Boundary representation and boundary condition imposition in the material point method. In A. Faramarzi, & S. Dirar (Eds.),
• Fan, L., Augarde, C. E., & Coombs, W. M. (2017). The point collocation method with a local maximum entropy approach. In A. Faramarzi, & S. Dirar (Eds.),
• crack propagation. In A. Faramarzi, & S. Dirar (Eds.), Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017): 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK (138-141)
• Robinson, S., Brown, M., Brennan, A., Cortis, M., Augarde, C., & Coombs, W. (2016). Improving seabed cable plough performance for offshore renewable energy. In C. Guedes Soares, (Ed.), Progress in renewable energies offshore : proceedings of the 2nd International Conference on Renewable Energies Offshore (RENEW2016), Lisbon, Portugal, 24-26 October 2016 (1-7). https://doi.org/10.1201/9781315229256
• Coombs, W. (2016). On the use of Plastic Inserts in Prestressed Railway Components. In J. Pombo (Ed.), Proceedings of the Third International Conference on Railway Technology: Research, Development and Maintenance. https://doi.org/10.4203/ccp.110.238
• Ghaffari Motlagh, Y., & Coombs, W. (2016). A high-order material point method. In Proceedings of the 24th UK Conference of the Association for Computational Mechanics in Engineering, 31 March - 01 April 2016, Cardiff University, Cardiff (352-355)
• Cortis, M., Coombs, W., & Augarde, C. (2016). Implicit essential boundaries in the Material Point Method. In Proceedings of the 24th UK Conference of the Association for Computational Mechanics in Engineering, 31 March - 01 April 2016, Cardiff University, Cardiff (116-119)
• Charlton, T., Coombs, W., & Augarde, C. (2016). Gradient elasticity with the material point method. In Proceedings of the 24th UK Conference of the Association for Computational Mechanics in Engineering, 31 March - 01 April 2016, Cardiff University, Cardiff (112-115)
• Mukwiri, R., Ghaffari Motlagh, Y., Coombs, W., & Augarde, C. (2016). Energy dissipation in granular material under 1D compression. In Proceedings of the 24th UK Conference of the Association for Computational Mechanics in Engineering, 31 March - 01 April 2016, Cardiff University, Cardiff (231-234)
• Bird, R., Coombs, W., & Giani, S. (2016). Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity. In Proceedings of the 24th UK Conference of the Association for Computational Mechanics in Engineering, 31 March - 01 April 2016, Cardiff University, Cardiff (137-140)
• Adams, T., Giani, S., & Coombs, W. (2016). Topology optimisation using level set methods and the discontinuous Galerkin method. In Proceedings of the 24th UK Conference of the Association for Computational Mechanics in Engineering, 31 March - 01 April 2016, Cardiff University, Cardiff (6-9)
• Robinson, S., Brown, M. J., Brennan, A. J., Cortis, M., Augarde, C. E., & Coombs, W. M. (2016). Development of low cost 3D soil surface scanning for physical modelling.
• Leung, A., Anastasopoulos, I., Augarde, C., Barreto, D., Brennan, A., Brown, M., …Zielinski, M. (2015). An overview of research activities and achievement in Geotechnics from the Scottish Universities Geotechnics Network (SUGN). In M. . G. Winter, D. . M. Smith, P. . J. . L. Eldred, & D. . G. Toll (Eds.), Geotechnical engineering for infrastructure and development : XVI European conference on soil mechanics and geotechnical engineering (4289-4294)
• Coombs, W. (2015). On isogeometric yield envelopes. In Computational Plasticity XIII proceedings of the XIII International Conference on Computational Plasticity - Fundamentals and Applications, held in Barcelona, Spain 1 - 3 September 2015
• Charlton, T. J., Coombs, W. M., & Augarde, C. E. (2015). On the implicit implementation of the Generalised Interpolation Material Point method. In A. J. Gil, & R. Sevilla (Eds.), Proceedings of the 23rd Conference on Computational Mechanics, ACME-UK 2015 (413-416)
• Coombs, W., & Crouch, R. (2014). Fabric anisotropy & DEM informed two-surface hyperplasticity: constitutive formulation, asymptotic states & experimental validation. In K. Soga, K. Kumar, G. Biscontin, & M. Kuo (Eds.), Geomechanics from micro to macro : IS-Cambridge 2014, 1-3 September, Cambridge, UK ; proceedings (777-782)
• Charlton, T., Coombs, W., & Augarde, C. (2014). A review of the Material Point Method and its links to other computational methods. In A. Javadi, & M. S. Hussain (Eds.), Proceedings of the 22nd UK National Conference of the Association for Computational Mechanics in Engineering, 2nd - 4th April 2014, University of Exeter, UK (17-20)
• Toll, D., & Hassan, A. (2014). Data Acquisition and Control Software for Automated Resistivity Measurements. In D. G. Toll, H. Zhu, A. Osman, W. Coombs, X. Li, & M. Rouainia (Eds.), Information Technology in Geo-Engineering (170-176). https://doi.org/10.3233/978-1-61499-417-6-170
• Asquith, J., & Toll, D. (2014). Data Acquisition Software for Controlling Serial Ports with Cloud Data Storage. In D. G. Toll, H. Zhu, A. Osman, W. Coombs, X. Li, & M. Rouainia (Eds.), Information Technology in Geo-Engineering (163-169). https://doi.org/10.3233/978-1-61499-417-6-163
• Coombs, W. (2013). Unique Critical State single-surface anisotropic hyperplasticity. In E. Onate, D. R. J. Owen, D. Peric, & B. Suarez (Eds.),
• Ullah, Z., Augarde, C., & Coombs, W. (2013). Three-dimensional FE-EFGM adaptive coupling and its applications in the nonlinear adaptive analysis. In A. Osman, I. Akkerman, C. Augarde, W. Coombs, R. Crouch, T. Koziara, & J. Trevelyan (Eds.),
• Coombs, W., Crouch, R., & Heaney, C. (2012). Plane-strain Mohr-Coulomb inelasticity. In Z. J. Yang (Ed.),
• Coombs, W., & Crouch, R. (2011). Reuleaux plasticity: improving Mohr-Coulomb and Drucker-Prager. In F. B. J. Barends, J. Breedeveld, R. B. J. Brinkgreve, M. Korff, & L. A. van Paassen (Eds.), Geotechnical engineering : new horizons, 21st European Young Geotechnical Engineers' Conference, 2011, Rotterdam ; proceedings (241-247). https://doi.org/10.3233/978-1-60750-808-3-241
• Coombs, W. M., Crouch, R. S., & Augarde, C. E. (2011). On the f fields of inadmissible stress space. In E. Oñate, D. R. J. Owen, D. Peric, & B. Suárez (Eds.), Computational plasticity XI: fundamentals and applications
• Coombs, W. M., Crouch, R. S., & Augarde, C. E. (2011). Unique Critical State Hyperplasticity. In O. Laghrouche, A. EL Kacimi, P. Woodward, & G. Medero (Eds.), Proceedings of the 19th UK National Conference of the Association for Computational Mechanics in Engineering : 5-6 April 2011, Heriot-Watt University, Edinburgh (49-52)
• Coombs, W., Crouch, R., & Augarde, C. (2010). 70-line 3D finite deformation elastoplastic finite-element code. In B. T., & N. S. (Eds.), Numerical methods in geotechnical engineering : proceedings of the seventh european conference on numerical methods in geotechnical engineering, Trondheim, Norway, 2-4 June 2010 (151-156). https://doi.org/10.1201/b10551-28
• Heaney, C., Augarde, C., Deeks, A., Coombs, W., & Crouch, R. (2010). Advances in meshless methods with application to geotechnics. In T. Benz, & S. Nordal (Eds.), Numerical Methods in Geotechnical Engineering (239-244)
• Coombs, W. M., Crouch, R. S., & Augarde, C. E. (2010). On the use of Reuleaux plasticity for geometric non-linear analysis. In A. Zervos (Ed.),
• Coombs, W., Crouch, R., & Augarde, C. (2009). Influence of Lode Angle Dependency on the Critical State for Rotational Plasticity. In E. Oñate, D. R. J. Owen, & B. Suárez (Eds.), X International Conference on Computational Plasticity (COMPLAS X)
• Coombs, W., Crouch, R., & Augarde, C. (2009). On the necessity for rotational yielding in anisotropic plasticity. In C. Sansour (Ed.), 17th UK Conference on Computational Mechanics (ACME-UK) (345-348)

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. Retrieved from 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. Netherlands: IOS Press

Journal Article

• 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, https://doi.org/10.1016/j.mechmat.2024.104958
• 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, https://doi.org/10.1002/nme.7438
• 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
• 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
• 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
• 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., …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. (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
• 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
• 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
• 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., …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., …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., …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. (2020). AMPLE: A Material Point Learning Environment. Advances in Engineering Software, 139, Article 102748. https://doi.org/10.1016/j.advengsoft.2019.102748
• 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., Brennan, A., Brown, M., Charlton, T., Knappett, J., …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
• 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., …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
• 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
• 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
• 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., & Augarde, C. (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., & Augarde, C. (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., & 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

Presentation

• 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
• Bird, R., Pretti, G., Coombs, W. M., Augarde, C. E., Sharif, Y., Brown, M., …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
• 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
• 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
• 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
• 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
• 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
• 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

Report

• Ullah, Z., Augarde, C., & Coombs, W. (2013). Local maximum entropy shape functions based FE-EFGM coupling. [No known commissioning body]