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Improving the Material-Point Method

  • Deborah SulskyEmail author
  • Ming Gong
Chapter
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 81)

Abstract

The material-point method (MPM) was introduced about 20 years ago and is a versatile method for solving problems in continuum mechanics. The flexibility of the method is achieved by combining two discretizations of the material. One is a Lagrangian description based on representing the continuum by a set of material points that are followed throughout the calculation. The second is a background grid that is used to solve the continuum equations efficiently. In its original form, some applications of the method appeared to be second order accurate while other tests showed poor or no convergence. This paper provides a framework for analyzing the errors in MPM. Moreover, the analysis suggests modifications to the algorithm to improve accuracy. The analysis also points to connections between MPM and other meshfree methods.

Keywords

Shape Function Material Point Deformation Gradient Quadrature Point Move Little Square 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was partially supported by the National Science Foundation under grant ARC 1023667 to the University of New Mexico.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe University of New MexicoAlbuquerqueUSA

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