Research Article

Solution of quasi-static large-strain problems by the material point method

  1. L. Beuth1,3,*,
  2. Z. Więckowski2,†,
  3. P. A. Vermeer1,3,‡

Article first published online: 30 SEP 2010

DOI: 10.1002/nag.965

Issue

International Journal for Numerical and Analytical Methods in Geomechanics

International Journal for Numerical and Analytical Methods in Geomechanics

Volume 35, Issue 13, pages 1451–1465, September 2011

Additional Information

How to Cite

Beuth, L., Więckowski, Z. and Vermeer, P. A. (2011), Solution of quasi-static large-strain problems by the material point method. Int. J. Numer. Anal. Meth. Geomech., 35: 1451–1465. doi: 10.1002/nag.965

Author Information

  1. 1

    Institute of Geotechnical Engineering, University of Stuttgart, Pfaffenwaldring 35, 70569 Stuttgart, Germany

  2. 2

    Department of Mechanics of Materials, Technical University of ódź, Al. Politechniki 6, 90-924 ódź, Poland

  3. 3

    Deltares, Stieltjesweg 2, 2600 MH Delft, The Netherlands

  1. †

    Associate Professor.

  2. ‡

    Professor Emeritus.

*Deltares, Stieltjesweg 2, 2600 MH Delft, The Netherlands

  1. †

    Associate Professor.

  2. ‡

    Professor Emeritus.

Publication History

  1. Issue published online: 24 AUG 2011
  2. Article first published online: 30 SEP 2010
  3. Manuscript Accepted: 28 JUN 2010
  4. Manuscript Revised: 16 JUN 2010
  5. Manuscript Received: 10 FEB 2010

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Keywords:

  • material point method;
  • finite element method;
  • meshless methods;
  • arbitrary Lagrangian–Eulerian formulation;
  • large strains;
  • implicit integration

SUMMARY

A procedure for solving quasi-static large-strain problems by the material point method is presented. Owing to the Lagrangian–Eulerian features of the method, problems associated with excessive mesh distortions that develop in the Lagrangian formulations of the finite element method are avoided. Three-dimensional problems are solved utilizing 15-noded prismatic and 10-noded tetrahedral elements with quadratic interpolation functions as well as an implicit integration scheme. An algorithm for exploiting the numerical integration procedure on the computational mesh is proposed. Several numerical examples are shown. Copyright © 2010 John Wiley & Sons, Ltd.

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