An efficient and locking-free material point method for three dimensional analysis with simplex elements

Lei Wang, William M. Coombs (Lead / Corresponding author), Charles Augarde, Michael Cortis, Michael J. Brown, Andrew J. Brennan, Jonathan A. Knappett, Craig Davidson, David Richards, David J. White, Anthony P. Blake

Research output: Contribution to journalArticlepeer-review


The Material Point Method is a relative newcomer to the world of solid mechanics modelling. Its key advantage is the ability to model problems having large deformations while being relatively close to standard finite element methods, however its use for realistic engineering applications will happen only if the material point can be shown to be both efficient and accurate (compared to standard finite element methods), when modelling complex geometries with a range of material models. In this paper we present developments of the standard material point method aimed at realising these goals. The key contribution provided here is the development of a material point method that avoids volumetric locking (arising from elastic or elastoplastic material behaviour) whilst using low order tetrahedral finite elements for the background computational mesh, hence allowing unstructured background grids to be used for complex geometries. We also show that these developments can be effectively parallelised to improve computational efficiency.
Original languageEnglish
JournalInternational Journal for Numerical Methods in Engineering
Early online date4 Apr 2021
Publication statusE-pub ahead of print - 4 Apr 2021


  • Material Point Method
  • Offshore
  • Shear vane
  • Surface footing
  • Volumetric locking
  • Finite deformatin mechanics
  • Parallel analysis

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