AI 中文总结
本研究将修正剑桥本构公式集成到基于广义有限差分法的无网格框架，通过体积与偏量应力的分区耦合，实现稳定的雪模拟，可应用于车辆-雪相互作用，为动态雪载荷模拟提供可靠基础。
AI 中文摘要
雪是一种复杂的地质材料，其宏观响应由密度、温度及其演化微观结构的拓扑结构决定。它的力学行为涵盖弹性、塑性、黏性及失效主导的多个状态，这给数值方法带来了重大挑战，数值方法需要模拟大变形、演化的自由表面以及复杂的边界相互作用。本研究首次将适用于雪的修正剑桥（Modified Cam-Clay）本构公式，集成到基于广义有限差分法（Generalized Finite Difference Method）的纯无网格强形式配点框架中。主要的方法学贡献是一种数值耦合方案，它将压力和速度的全局隐式混合公式与本构回映算法相结合：静水压力项由泊松方程求得，随后通过修正剑桥（Modified Cam-Clay）回映程序进行校正；而偏量响应则采用数值黏性公式以半隐式方式处理。这种对体积应力和偏量应力项的分区处理，使得模拟能够使用相对较大的时间步长保持稳定，同时生成平滑的空间压力场，进而可精确评估复杂边界几何上的作用力。该耦合方案的数值结果表明，该框架具有算法稳定性、能有效施加边界条件，且适用于局部空间加密；同时还展示了该框架通过刚体耦合应用于车辆-雪相互作用的可行性。所提出的公式为未来车辆结构承受动态雪载荷的模拟提供了可靠基础。
英文摘要
Snow is a complex geomaterial whose macroscopic response is governed by density, temperature, and the topology of its evolving microstructure. Its mechanical behavior spans elastic, plastic, viscous, and failure dominated regimes, imposing significant challenges for numerical methods, which intends to simulate large deformations, evolving free surfaces, and complex boundary interactions. This work presents the first integration of a Modified Cam-Clay constitutive formulation for snow into a purely meshfree strong-form collocation framework based on the Generalized Finite Difference Method. The main methodological contribution is a numerical coupling that combines a global implicit mixed formulation for pressure and velocity with a constitutive return-mapping algorithm. The hydrostatic pressure contribution is obtained from a Poisson equation and subsequently corrected through the Modified Cam-Clay return-mapping procedure, while the deviatoric response is treated semi-implicitly using a numerical viscosity formulation. This partitioned treatment of the volumetric and deviatoric stress contributions enables stable simulations with comparatively large time steps while producing smooth spatial pressure fields. As a result, forces on complex boundary geometries can be evaluated accurately. Numerical results of this coupling illustrate the algorithmic stability of the framework, the effective imposition of boundary conditions, and the suitability of local spatial refinement. The feasibility of applying the framework to vehicle-snow interaction through rigid-body coupling is also illustrated. The presented formulation provides a robust basis for future simulations of dynamic snow loading on vehicle structures.
Comments37 pages, 19 figures, Preprint submitted to Computer Methods in Applied Mechanics and Engineering (CMAME)
