The Material Point Method is a relative newcomer to the world of solid mechanics modelling. Its key advantage is the ability to model problems having large deformations while being relatively close to standard finite element methods, however its use for realistic engineering applications will happen only if the material point can be shown to be both efficient and accurate (compared to standard finite element methods), when modelling complex geometries with a range of material models. In this paper we present developments of the standard material point method aimed at realizing these goals. The key contribution provided here is the development of a material point method that avoids volumetric locking (arising from elastic or elasto-plastic material behavior) while using low-order tetrahedral finite elements for the background computational mesh, hence allowing unstructured background grids to be used for complex geometries. We also show that these developments can be effectively parallelized to improve computational efficiency.

中文翻译：

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一种用于单形单元三维分析的高效无锁定材料点方法

材料点法是固体力学建模领域的一个新来者。它的主要优势是能够模拟具有大变形的问题，同时相对接近标准有限元方法，但是只有当材料点可以被证明既有效又准确（与标准有限元方法相比）时，它才会用于实际工程应用。元素方法），当使用一系列材料模型对复杂几何进行建模时。在本文中，我们介绍了旨在实现这些目标的标准物质点方法的发展。此处提供的关键贡献是开发了一种材料点方法，该方法避免了体积锁定（由弹性或弹塑性材料行为引起），同时将低阶四面体有限元用于背景计算网格，因此允许将非结构化背景网格用于复杂的几何形状。我们还表明，这些发展可以有效地并行化以提高计算效率。