This paper develops a novel Hybrid Particle Element Method (HPEM) to model large deformation problems in solid mechanics, combining the strengths of both mesh-based and particle approaches. In the proposed method, the computational domain is discretized into two independent components: a set of finite elements and a set of particles. The finite elements serve as a temporary tool to compute the spatial derivatives of field variables, while the particles are used for storing history variables and establishing equilibrium equations. Spatial derivatives of field variables on particles are obtained by averaging the surrounding Gauss points of finite elements with a smoothing function. When the finite element mesh becomes distorted, it can be arbitrarily adjusted or completely regenerated. No global variable mapping is required when mesh adjustment or regeneration is performed, thus avoiding irreversible interpolation errors. The proposed method is validated through six typical examples, assessing its accuracy, efficiency, and robustness. The superior performance of the proposed method is comprehensively demonstrated through comparisons with several existing numerical methods.

中文翻译：

---

一种用于固体力学中大变形分析的新型混合粒子单元方法 （HPEM）


本文开发了一种新颖的混合粒子元方法 （HPEM） 来模拟固体力学中的大变形问题，结合了基于网格的方法和粒子方法的优势。在所提出的方法中，计算域被离散为两个独立的组件：一组有限元和一组粒子。有限元用作计算场变量空间导数的临时工具，而粒子则用于存储历史变量和建立平衡方程。粒子上场变量的空间导数是通过用平滑函数对有限元的周围高斯点求平均值来获得的。当有限元网格变形时，可以任意调整或完全重新生成。执行网格调整或重新生成时不需要全局变量映射，从而避免了不可逆的插值误差。通过六个典型示例验证了所提出的方法，评估了其准确性、效率和鲁棒性。通过与几种现有数值方法的比较，全面证明了所提方法的优越性能。