The material point method (MPM) is a hybrid particle‐mesh scheme conceptually placed between mesh‐based and mesh‐free methods, combining aspects of both and well suited to solving large deformation engineering problems involving history‐dependent material models. A unique drawback of the MPM is the cell crossing error whereby material points crossing grid cells suddenly produce spurious stress oscillations leading to significant errors. After distilling the necessary conditions required for the cell crossing error, a novel quadrature‐based C₀ enhancement scheme is proposed. The partitioned quadrature material point method (PQMPM) effectively mitigates the cell crossing error while retaining the linear Lagrangian basis and Dirac density function of the original MPM, rendering it easily integrable into existing MPM codebases. One and two‐dimensional examples illustrate the elimination of the cell crossing error, improvement of solution accuracy (particularly reliable stress prediction), local application of the scheme across dynamically varying arbitrary spatial and temporal regions and the reasonable additional computational costs against increased accuracy. Contrasting existing enhanced MPM schemes, the PQMPM only incurs additional computational cost exactly when and where cell crossing errors would otherwise occur and minimally diffuses local effects.

中文翻译：

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物质点法精馏的细胞交叉误差导致基于正交的新型C0补救方法

材质点方法（MPM）是概念上介于基于网格的方法和基于无网格的方法之间的混合粒子网格方案，两者结合起来，非常适合解决涉及历史依赖的材料模型的大型变形工程问题。MPM的一个独特缺点是单元交叉误差，即跨网格单元的物料点突然产生虚假的应力振荡，从而导致明显的误差。在提取出细胞交叉误差所需的必要条件后，一种基于正交的新型C ₀提出了增强方案。分区正交材料点方法（PQMPM）在保留原始MPM的线性拉格朗日基和Dirac密度函数的同时，有效减轻了单元交叉误差，使其易于集成到现有MPM代码库中。一维和二维示例说明了单元交叉误差的消除，求解精度的提高（尤其是可靠的应力预测），跨动态变化的任意时空区域的局部应用方案以及针对提高精度的合理附加计算成本。与现有的增强型MPM方案相比，PQMPM仅在发生单元交叉错误的时间和地点准确地产生了额外的计算成本，并且最小化了局部影响。