Abstract The two types of numerical techniques related to the Material Point Method (MPM) are reported; one is the alternative interpolation function called Arbitrary Particle Domain Interpolation (APDI), and the other is the particle-element coupled method. APDI interpolation function is one of the domain integration methods, which can consider the arbitrary shape of particle domain in MPM. The numerical domain integration employed in APDI method has realized the simpler algorithm in both 2- or 3-dimensional implementation. Especially in 3-dimensional formulation, the simple formulation and implementation is inevitable for the integrity of the numerical method. On the other hand, the particle-element coupled method is the numerical framework to reduce the computational cost such as memory, storage and computational time. The basic idea of the particle-element method is to divide the target domain physically into subdomains, and they are combined together numerically by using the numerical grid. This technique enables us to apply the different interpolation function to the different parts of the target domain, realizing the complex calculation using both particle and element in the same procedure. In this paper, the formulations and the demonstrations of both APDI method and the particle-element coupled method are reported, and the applicability and effectiveness of the methods to geomaterial are clarified.

中文翻译：

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任意粒子域插值方法及其在岩土变形问题中的应用

摘要 报告了与物质点法 (MPM) 相关的两种数值技术；一种是称为任意粒子域插值（APDI）的替代插值函数，另一种是粒子-元素耦合方法。APDI插值函数是域积分方法之一，可以考虑MPM中粒子域的任意形状。APDI 方法中采用的数值域集成在 2 维或 3 维实现中实现了更简单的算法。尤其是在三维公式中，对于数值方法的完整性来说，简单的公式化和实现是不可避免的。另一方面，粒子-元耦合方法是降低内存、存储和计算时间等计算成本的数值框架。粒子元法的基本思想是将目标域物理上划分为子域，并利用数值网格将它们进行数值组合。这种技术使我们能够对目标域的不同部分应用不同的插值函数，在同一过程中实现粒子和元素的复杂计算。本文报道了APDI法和粒元耦合法的公式和论证，阐明了这些方法在岩土材料中的适用性和有效性。这种技术使我们能够对目标域的不同部分应用不同的插值函数，在同一过程中实现粒子和元素的复杂计算。本文报道了APDI法和粒元耦合法的公式和论证，阐明了这些方法在岩土材料中的适用性和有效性。这种技术使我们能够对目标域的不同部分应用不同的插值函数，在同一过程中实现粒子和元素的复杂计算。本文报道了APDI法和粒元耦合法的公式和论证，阐明了这些方法在岩土材料中的适用性和有效性。