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A critical assessment and contact algorithm for the staggered grid material point method
International Journal of Mechanics and Materials in Design ( IF 3.7 ) Pub Date : 2021-06-19 , DOI: 10.1007/s10999-021-09557-7
Lei Kan , Yong Liang , Xiong Zhang

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.



中文翻译:

交错网格材料点法的临界评估与接触算法

材料点法 (MPM) 已证明其是一种模拟大变形极端事件的有效数值方法。然而,原始的 MPM 存在由粒子正交引起的几个缺陷,包括单元交叉噪声、低空间集成精度和空间收敛性损失。我们新开发的交错网格材料点方法(SGMP)采用单元中心正交有效地消除单元交叉噪声并恢复空间收敛。在本文中,SGMP 进一步制定了更新应力最后、更新应力优先和修改后更新应力最后方案。分析导出不同方案的SGMP的能量误差,以研究其准确性和稳定性。通过从理论上和数值上研究其收敛性、稳定性、耗散和效率方面的性能,对 SGMP 的性能进行了严格的评估。该研究表明,SGMP 的性能比 MPM 好得多。此外,还为 SGMP 开发了一种接触算法来模拟接触影响问题,并通过几个数值例子进行验证。

更新日期:2021-06-19
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