材料点法的高效局部隐式接触算法

Local implicit contact algorithm in the material point method

材料点法(MPM)应用于散体材料数值模拟时,如采用完全显式接触算法,则不能维持系统机械能守恒,计算稳定性差。该文提出一种高效局部隐式接触算法,仅需求解局部接触方程组。采用这种接触算法的MPM能真实模拟多物体颗粒之间的各种相互作用,包括挤压、摩擦滑移、分离等过程,正确反映接触规律。理论分析和计算结果表明,局部隐式接触算法与完全显式接触算法相比,计算过程数值稳定,计算效率高,系统机械能保持守恒。

The standard material point method using an explicit contact algorithm for numerical simulations of the motion of granular materials often results in a large computational cost and numerical instabilities. An efficient local implicit contact algorithm is given that only solves local contact equations to determine the contact forces. The material point method with the local implicit contact algorithm can be used in exactly numerical simulations of the mechanical behavior of granular materials. Interaction between grains, including impact, friction, and separation can be modeled. Both theoretical and computational results show better numerical stability, energy conservation, and higher efficiency of local implicit contact algorithm than the explicit contact algorithm.