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A critical assessment and contact algorithm for the staggered grid material point method

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Abstract

The material point method (MPM) has demonstrated itself as an effective numerical method to simulate extreme events with large deformations. However, the original MPM suffers several defects caused by the particle quadrature, including cell crossing noise, low spatial integration accuracy, and loss of spatial convergence. Our newly developed staggered grid material point method (SGMP) employs the cell center quadrature to efficiently eliminate the cell crossing noise and to recover the spatial convergence. In this paper, the SGMP is further formulated with the updated stress last, updated stress first and modified updated stress last schemes. The energy errors of the SGMP with different schemes are derived analytically to study their accuracy and stability. The performance of the SGMP is critically assessed by investigating its performance in terms of convergence, stability, dissipation and efficiency theoretically and numerically. This study shows that the SGMP performs much better than the MPM. In addition, a contact algorithm is also developed for the SGMP to model the contact-impact problems, and is verified by several numerical examples.

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Authors and Affiliations

  1. School of Aerospace Engineering, Tsinghua University, Beijing, 100084, People’s Republic of China

    Lei Kan & Xiong Zhang

  2. Department of Civil and Environmental Engineering, University of California, Berkeley, CA, 94720, USA

    Yong Liang

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  1. Lei Kan
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  2. Yong Liang
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Correspondence to Xiong Zhang.

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Supported by the National Natural Science Foundation of China (11672154).

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Kan, L., Liang, Y. & Zhang, X. A critical assessment and contact algorithm for the staggered grid material point method. Int J Mech Mater Des 17, 743–766 (2021). https://doi.org/10.1007/s10999-021-09557-7

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  • DOI: https://doi.org/10.1007/s10999-021-09557-7

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