Mitigating kinematic locking in the material point method

  • Authors:

  • C. M. Mast;P. Mackenzie-Helnwein;P. Arduino;G. R. Miller;W. Shin

  • Affiliations:

  • Department of Civil & Environmental Engineering, University of Washington, Box 352700, Seattle, WA 98195-2700, USA;Department of Civil & Environmental Engineering, University of Washington, Box 352700, Seattle, WA 98195-2700, USA;Department of Civil & Environmental Engineering, University of Washington, Box 352700, Seattle, WA 98195-2700, USA;Department of Civil & Environmental Engineering, University of Washington, Box 352700, Seattle, WA 98195-2700, USA;Shannon & Wilson, Inc., 400 North 34th Street, Suite 100, Seattle, WA 98103, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

The material point method exhibits kinematic locking when traditional linear shape functions are used with a rectangular grid. The locking affects both the strain and the stress fields, which can lead to inaccurate results and nonphysical behavior. This paper presents a new anti-locking approach that mitigates the accumulation of fictitious strains and stresses, significantly improving the kinematic response and the quality of all field variables. The technique relies on the Hu-Washizu multi-field variational principle, with separate approximations for the volumetric and the deviatoric portions of the strain and stress fields. The proposed approach is validated using a series of benchmark examples from both solid and fluid mechanics, demonstrating the broad range of modeling possibilities within the MPM framework when combined with appropriate anti-locking techniques and algorithms.