Open Access

ARTICLE

Material Point Method with RBF Interpolation

by Htike¹, Wen Chen¹, Yan Gu¹, Junjie Yang¹

1 Centre for Numerical Simulation Software in Engineering and Sciences, Department of Engineering Mechanics, Hohai University, Nanjing 210098, China

Computer Modeling in Engineering & Sciences 2011, 72(4), 247-272. https://doi.org/10.3970/cmes.2011.072.247

Abstract

This paper makes the first attempt to employ the Radial Basis Function (RBF) interpolation in the material point method (MPM), in which the shape function is based on RBF and polynomial function and satisfies the partition of unity and possesses Delta-function property. It is worthy of stressing that the RBF interpolation has the merit of high smoothness and is very accurate and can easily be applied to the MPM framework for mapping information between moving particles, known as material point in the MPM, and background grids. The RBF-based MPM is designed to overcome the unphysical results, such as shear stress distribution of the cantilever beam, in the traditional MPM with linear shape function. This study chooses the Mutiquadric (MQ) function as the RBF. The present strategy is tested to the benchmark cantilever beam and the circular disk impact problems. Numerical results are observed in good agreement with the analytical solutions and satisfy the conservation of energy.

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Keywords

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