Although grid-based particle methods are widely used for engineering deformation problems, due to their robustness in large deformation analyses, the computational cost of these methods is quite high compared with mesh-based methods. In 3D problems, the computational cost becomes even higher, whereas some mechanical systems can be regarded as axisymmetric, allowing them to be modeled as two-dimensional axisymmetric entities, resulting in a reduced computation cost. In order to decrease the computational cost further, arbitrary spatial discretization has been introduced to reduce the degrees of freedom in the system. The Particle-Element Coupled Method (PEM), the coupled method of the Material Point Method (MPM) and the Arbitrary Particle Domain Interpolation (APDI) method, enables a system to be discretized in arbitrary spatial resolutions. In this paper, PEM is extended to axisymmetric problems, whose formulation and applicability to geomaterial deformation are presented. Firstly, the axisymmetric MPM simulation of a granular column collapse experiment and its efficiency in computation are reported. Secondly, in the simulation of footing penetration, it is shown that the axisymmetric MPM and the axisymmetric PEM can be used to analyze large deformations that cannot be analyzed by mesh-based methods, such as the Finite Difference Method (FDM). The axisymmetric PEM yields equivalent average pressure–displacement relationships and shear strain distributions, realizing a reduction in the computation cost by half as much.

尽管基于网格的粒子方法被广泛用于工程变形问题，但由于它们在大变形分析中的鲁棒性，与基于网格的方法相比，这些方法的计算成本相当高。在 3D 问题中，计算成本变得更高，而一些机械系统可以被视为轴对称，允许将它们建模为二维轴对称实体，从而降低计算成本。为了进一步降低计算成本，引入了任意空间离散化来降低系统的自由度。粒子-元素耦合方法 (PEM) 是物质点方法 (MPM) 和任意粒子域插值 (APDI) 方法的耦合方法，能够以任意空间分辨率对系统进行离散化。在本文中，PEM 扩展到轴对称问题，提出了其公式和对地质材料变形的适用性。首先，报告了颗粒柱塌陷实验的轴对称MPM模拟及其计算效率。其次，在基础穿透的模拟中，表明轴对称 MPM 和轴对称 PEM 可用于分析基于网格的方法无法分析的大变形，例如有限差分法 (FDM)。轴对称 PEM 产生等效的平均压力-位移关系和剪切应变分布，将计算成本降低了一半。报告了颗粒柱塌陷实验的轴对称 MPM 模拟及其计算效率。其次，在基础穿透的模拟中，表明轴对称 MPM 和轴对称 PEM 可用于分析基于网格的方法无法分析的大变形，例如有限差分法 (FDM)。轴对称 PEM 产生等效的平均压力-位移关系和剪切应变分布，将计算成本降低了一半。报告了颗粒柱塌陷实验的轴对称 MPM 模拟及其计算效率。其次，在基础穿透的模拟中，表明轴对称 MPM 和轴对称 PEM 可用于分析基于网格的方法无法分析的大变形，例如有限差分法 (FDM)。轴对称 PEM 产生等效的平均压力-位移关系和剪切应变分布，将计算成本降低了一半。例如有限差分法（FDM）。轴对称 PEM 产生等效的平均压力-位移关系和剪切应变分布，将计算成本降低了一半。例如有限差分法（FDM）。轴对称 PEM 产生等效的平均压力-位移关系和剪切应变分布，将计算成本降低了一半。