Imposition of essential boundary conditions in the material point method

Michael Cortis (Lead / Corresponding author), William M. Coombs, Charles E. Augarde, Michael Brown, Andrew Brennan, Scott Robinson

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44 Citations (Scopus)
249 Downloads (Pure)


There is increasing interest in the material point method (MPM) as a means of modelling solid mechanics problems in which very large deformations occur, e.g. in the study of landslides and metal forming; however, some aspects vital to wider use of the method have to date been ignored, in particular methods for imposing essential boundary conditions in the case where the problem domain boundary does not coincide with the background grid element edges. In this paper, we develop a simple procedure originally devised for standard finite elements for the imposition of essential boundary conditions, for the MPM, expanding its capabilities to model boundaries of any inclination. To the authors' knowledge, this is the first time that a method has been proposed that allows arbitrary Dirichlet boundary conditions (zero and nonzero values at any inclination) to be imposed in the MPM. The method presented in this paper is different from other MPM boundary approximation approaches, in that (1) the boundaries are independent of the background mesh, (2) artificially stiff regions of material points are avoided, and (3) the method does not rely on mirroring of the problem domain to impose symmetry. The main contribution of this work is equally applicable to standard finite elements and the MPM.

Original languageEnglish
Pages (from-to)130-152
Number of pages23
JournalInternational Journal for Numerical Methods in Engineering
Issue number1
Early online date21 Jun 2017
Publication statusPublished - 6 Jan 2018


  • embedded boundaries
  • material point method
  • nonmatching meshes

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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