Open Access

ARTICLE

Multiscale Simulations Using Generalized Interpolation Material Point (GIMP) Method And SAMRAI Parallel Processing

J. Ma¹, H. Lu¹, B. Wang¹, S. Roy¹, R. Hornung², A. Wissink², R. Komanduri^1,3

1 School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, U.S.A
2 Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551, U.S.A
3 Correspondence author, e-mail:ranga@ceat.okstate.edu; Tel: 405-744-5900; Fax: 405-744-7873.
This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48. UCRL-JRNL-208241.

Computer Modeling in Engineering & Sciences 2005, 8(2), 135-152. https://doi.org/10.3970/cmes.2005.008.135

Abstract

In the simulation of a wide range of mechanics problems including impact/contact/penetration and fracture, the material point method (MPM), Sulsky, Zhou and Shreyer (1995), demonstrated its computational capabilities. To resolve alternating stress sign and instability problems associated with conventional MPM, Bardenhagen and Kober (2004) introduced recently the generalized interpolation material point (GIMP) method and implemented for one-dimensional simulations. In this paper we have extended GIMP to 2D and applied to simulate simple tension and indentation problems. For simulations spanning multiple length scales, based on the continuum mechanics approach, we present a parallel GIMP computational method using the Structured Adaptive Mesh Refinement Application Infrastructure (SAMRAI). SAMRAI is used for multi-processor distributed memory computations, as a platform for domain decomposition, and for multi-level refinement of the computational domain. Nested computational grid levels (with successive spatial and temporal refinements) are used in GIMP simulations to improve the computational accuracy and to reduce the overall computational time. The domain of each grid level is divided into multiple rectangular patches for parallel processing. This domain decomposition embedded in SAMRAI is very flexible when applied to GIMP. As an example to validate the parallel GIMP computing scheme under SAMRAI parallel computing environment, numerical simulations with multiple length scales from nanometer to millimeter were conducted on a 2D nanoindentation problem. A contact algorithm in GIMP has also been developed for the treatment of contact pair between a rigid indenter and a deformable workpiece. GIMP results are compared with finite element results on indentation for validation. A GIMP nanoindentation problem with five levels of refinement was modeled using multi-processors to demonstrate the potential capability of the parallel GIMP computation.

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