论文标题
明确的材料点方法规避体积锁定：一种简单，高效且通用的方法
Circumventing volumetric locking in explicit material point methods: A simple, efficient, and general approach
论文作者
论文摘要
材料点方法（MPM）经常用于模拟几乎不可压缩材料的大变形，例如水，橡胶和未排水的多孔介质。但是，几乎不可压缩材料的MPM解决方案容易容易容易体积锁定，也就是说，与错误的应变和应力场过于坚硬的行为。尽管已经设计了几种方法来减轻MPM中的体积锁定，但它们需要对现有MPM机械进行重大修改，这通常是针对某些基础功能或材料类型量身定制的。在这项工作中，我们提出了一种锁定方法，该方法具有前所未有的简单性，功效和一般性的组合，适用于一个明确的MPM配方家族。该方法结合了假定的变形梯度（$ \ bar {\ boldsymbol {f}} $）方法与MPM中标准粒子网格传输方案构建的音量平均操作。在明确的时间集成后，这种组合产生了一种新的简单算法，用于更新变形梯度，并保留所有其他MPM过程。因此，提出的方法易于实施，低成本和与MPM中现有机械兼容。通过固体和流体力学中几乎不可压缩的问题，我们验证所提出的方法是否有效地规避了显式MPM中的体积锁定，无论其基本功能和材料类型如何。
The material point method (MPM) is frequently used to simulate large deformations of nearly incompressible materials such as water, rubber, and undrained porous media. However, MPM solutions to nearly incompressible materials are susceptible to volumetric locking, that is, overly stiff behavior with erroneous strain and stress fields. While several approaches have been devised to mitigate volumetric locking in the MPM, they require significant modifications of the existing MPM machinery, often tailored to certain basis functions or material types. In this work, we propose a locking-mitigation approach featuring an unprecedented combination of simplicity, efficacy, and generality for a family of explicit MPM formulations. The approach combines the assumed deformation gradient ($\bar{\boldsymbol{F}}$) method with a volume-averaging operation built on the standard particle-grid transfer scheme in the MPM. Upon explicit time integration, this combination yields a new and simple algorithm for updating the deformation gradient, preserving all other MPM procedures. The proposed approach is thus easy to implement, low-cost, and compatible with the existing machinery in the MPM. Through various types of nearly incompressible problems in solid and fluid mechanics, we verify that the proposed approach efficiently circumvents volumetric locking in the explicit MPM, regardless of the basis functions and material types.
