Fully implicit, stabilised, three-field material point method for dynamic coupled problems

Xiangcou Zheng, Federico Pisanò, Philip J. Vardon, Michael A. Hicks*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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This study presents the formulation and implementation of a fully implicit stabilised Material Point Method (MPM) for dynamic problems in two-phase porous media. In particular, the proposed method is built on a three-field formulation of the governing conservation laws, which uses solid displacement, pore pressure and fluid displacement as primary variables (u–p–U formulation). Stress oscillations associated with grid-crossing and pore pressure instabilities near the undrained/incompressible limit are mitigated by implementing enhanced shape functions according to the Generalised Interpolation Material Point (GIMP) method, as well as a patch recovery of pore pressures – from background nodes to material points – based on the same Moving Least Square Approximation (MLSA) approach investigated by Zheng et al. [1]. The accuracy and computational convenience of the proposed method are discussed with reference to several poroelastic verification examples, spanning different regimes of material deformation (small versus large) and dynamic motion (slow versus fast). The computational performance of the proposed method in combination with the PARDISO solver for the discrete linear system is also compared to explicit MPM modelling [1] in terms of accuracy, convergence rate, and computation time.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalEngineering with Computers
Publication statusPublished - 2022


  • Coupled poromechanics
  • Implicit time integration
  • Material point method
  • Patch recovery
  • Pore pressure stabilisation


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