Time steps for explicit MPM simulation in computer graphics are often selected by trial and error due to the challenges in automatically selecting stable time step sizes. Our time integration scheme uses time step restrictions that take into account forces, collisions, and even grid‐to‐particle transfers calculated near the end of the time step. We propose a novel set of time step restrictions that allow a time step to be selected that is stable, efficient to compute, and not too far from optimal. We derive the general solution for the sound speed in nonlinear isotropic hyperelastic materials, which we use to enforce the classical CFL time step restriction. We identify a single‐particle instability in explicit MPM integration and propose a corresponding time step restriction in the fluid case. We also propose a reflection‐based boundary condition for domain walls that supports separation and accurate Coulomb friction while preventing particles from penetrating the domain walls.

中文翻译：

---

显式 MPM 模拟的有效时间步长限制

由于自动选择稳定时间步长的挑战，计算机图形学中显式 MPM 模拟的时间步长通常通过反复试验来选择。我们的时间积分方案使用时间步长限制，这些限制考虑了在时间步长结束时计算的力、碰撞，甚至是网格到粒子的传输。我们提出了一组新颖的时间步长限制，允许选择一个稳定、计算高效且离最优值不太远的时间步长。我们推导出非线性各向同性超弹性材料中声速的一般解，我们用它来强制执行经典的 CFL 时间步长限制。我们确定了显式 MPM 积分中的单粒子不稳定性，并在流体情况下提出了相应的时间步长限制。