一种用于可变形粒子模拟的变分公式及其水平集离散元法实现
A Variational Formulation for Deformable Particle Simulations and its Level Set Discrete Element Method Implementation
AI总结：
本文提出了一种基于变分公式的可变形离散元方法，通过水平集方法实现颗粒变形，保留了经典DEM的稳健性和可扩展性，同时在计算成本相近的情况下实现了物理合理的颗粒尺度变形。
摘要：
我们提出了一种可变形的离散元法（DEM），通过降低阶的弹性颗粒尺度变形描述扩展了经典的刚性粒子公式。该方法依赖于两个发展。首先，基于拉格朗日-达朗贝尔原理的能耗变分公式将经典刚体动力学扩展到包含粒子变形性，通过在统一的能耗描述中嵌入平移、旋转和变形自由度。其次，通过演化的水平集实现粒子变形。该框架适用于一般颗粒几何形状和拓扑结构，支持任意变形模式。所得的可变形DEM保留了经典DEM的稳健性、几何和物理清晰度以及可扩展性，同时在计算成本与刚性DEM相当的情况下，实现了物理上合理的颗粒尺度变形性。与完整有限元模拟的比较在粒子和系统尺度上均显示出良好的一致性，建立了用于颗粒系统变形建模的一般且可扩展的变分框架。
英文摘要：
We present a deformable Discrete Element Method (DEM) that extends the classical rigid-particle formulation through a reduced-order description of elastic grain-scale deformation. The method hinges on two developments. First, an energetic variational formulation based on the Lagrange--d'Alembert principle extends classical rigid-body dynamics to incorporate particle deformability by embedding translational, rotational, and deformation degrees of freedom within a unified energetic description. Second, particle deformation is realized within the Level Set DEM formalism through evolving level sets. The framework applies broadly to general particle geometries and topologies, and supports arbitrary deformation modes. The resulting deformable DEM retains the robustness, geometric and physical clarity, and scalability of classical DEM, while enabling physically grounded grain-scale deformability at a computational cost of the same order of magnitude as rigid DEM. Comparisons with full finite-element simulations demonstrate excellent agreement at both particle and system scales, establishing a general and extensible variational framework for modeling deformation in particulate systems.
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