Implementing Dynamic Boundary Conditions with the Material Point Method

Phuong Chinh Do, Philip J. Vardon*, José León González Acosta, Michael A. Hicks

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review


The material point method (MPM) is gaining an increasing amount of attention due to its capacity to solve geotechnical problems involving large deformations. Large deformations in geotechnics usually involve the failure process and therefore dynamic analyses are often carried out. However, simulating the (infinite) continuous domain using typical Dirichlet (fixed) boundary conditions induces spurious reflections, causing (1) unrealistic stress increments at the domain boundary and (2) the appearance of multiple unnatural stress waves in the domain. Aiming to eliminate this numerical artifact in MPM, two solutions for absorbing boundary conditions found in FEM are implemented and investigated; these are (1) a viscous boundary condition and (2) a viscoelastic boundary condition. The use of such dynamic boundary conditions in MPM is scarce and no validation of them has yet been presented in the literature. In this paper, these absorbing conditions are implemented alongside recent mapping and integration techniques, improving numerical stability and accuracy.

Original languageEnglish
Title of host publicationChallenges and Innovations in Geomechanics
Subtitle of host publicationProceedings of the 16th International Conference of IACMAG
EditorsMarco Barla, Alessandra Insana, Alice Di Donna, Donatella Sterpi
PublisherSpringer Science
Number of pages8
ISBN (Print)9783031128509
Publication statusPublished - 2023
Event6th International Conference of the International Association for Computer Methods and Advances in Geomechanics, IACMAG 2022 - Turin, Italy
Duration: 30 Aug 20222 Sep 2022

Publication series

NameLecture Notes in Civil Engineering
Volume288 LNCE
ISSN (Print)2366-2557
ISSN (Electronic)2366-2565


Conference6th International Conference of the International Association for Computer Methods and Advances in Geomechanics, IACMAG 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Double mapping–generalized composite MPM
  • Dynamic boundaries
  • Implicit MPM
  • Shallow foundation
  • Wave propagation


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