[最新文献]材料点法(MPM)隐式接触技术的发展[12/15/2020]

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1 论文

Development of an implicit contact technique for the material point method 材料点法隐式接触技术的发展

Abstract: An implicit contact algorithm for the material point method (MPM) has been developed to simulate contact. This allows recently developed implicit MPM codes to simulate large-scale deformations and interaction with external bodies. The performance of the method has been investigated and compared to an existing explicit method using benchmark and geotechnical examples. In particular, the proposed formulation has been shown to conserve energy in a similar way to the explicit formulation and reach similar results. The method typically converges to the analytical solution when an adequate time step and mesh size are used, with the time step generally being around ten times larger than the explicit method, although during the contact phase this does not always result in faster computation due to the iterative solution procedure.

Keywords: Contact simulation, Frictional contact, Implicit scheme, Material point method, Soil-structure interaction

摘要：发展了一种材料点法（MPM）的隐式接触算法来模拟接触, 这使得最近开发的隐式MPM代码能够模拟大规模变形和与外部机构的相互作用。研究了该方法的性能，并利用基准和岩土实例与现有的显式方法进行了比较。特别是，所提出的公式已被证明以类似于显式公式的方式节省能量，并达到类似的结果。当使用适当的时间步长和网格大小时，该方法通常会收敛到分析解，时间步长一般是显式方法的10倍左右，尽管在接触阶段，由于迭代求解程序，这并不总是导致更快的计算。

2 相关文献

Note: '相关文献' 是按照Google的排序算法产生出来的.

[1] Development of an implicit material point method for geotechnical applications

[2] Implicit Dynamics in the Material-Point Method

[3] Incompressible material point method for free surface flow

[4] Implicit time integration for the material point method: Quantitative and algorithmic comparisons with the finite element method

[5] The Material Point Method for Simulating Continuum Materials

[6] Modeling Landslide-Induced Flow Interactions with Structures using the Material Point Method

[7] MPM with frictional contact for application to soft particulate materials

[8] On the practical use of the Material Point Method for offshore geotechnical applications

[9] An Implicit Material Point Method Applied to Granular Flows

[10] Issues with the Material Point Method for the modelling of geotechnical processes, and how to solve them

3 材料点法(MPM)简介

材料点法(MPM)是一种用于模拟固体、液体、气体和任何其他连续体材料行为的数值技术。特别地，它是模拟多相（固-液-气）相互作用的一种稳健的空间离散方法。在MPM中，一个连续体是由一些小的拉格朗日元素描述的，称为 "材料点"。这些材料点被背景网格包围，该网格仅用于计算梯度项，如变形梯度。与其他基于网格的方法，如有限元法(如Abaqus)、有限体积法(如FLAC3D)或有限差分法(如3DEC)不同，MPM不是基于网格的方法，而是被归类为无网格/无网格或基于连续体的粒子方法，其中的例子是平滑粒子流体力学(SPH)和过动力学(Peridynamics)。尽管有背景网格的存在，但MPM并没有遇到基于网格方法的缺点（如大变形纠结、平移误差等），这使它成为计算力学中一个有前途的强大工具。

MPM最初是由新墨西哥大学(University of New Mexico)的Deborah L.Sulsky教授、陈振教授和Howard L.Schreyer教授在1990年初提出的，是PIC {Particle-in-Cell}的方法的进一步扩展以及在计算固体动力学中的延伸。在这一初步发展之后，MPM在美国一些国家实验室以及新墨西哥大学、俄勒冈州立大学、犹他大学等和世界范围内都得到了进一步的发展。

MPM已经在岩土边坡和隧道稳定性研究中得到了应用.