Dynamics simulation with frictional contacts is important for a wide range of applications, from cloth simulation to object manipulation. Recent methods using smoothed lagged friction forces have enabled robust and differentiable simulation of elastodynamics with friction. However, the resulting frictional behavior can be inaccurate and may not converge to analytic solutions. Here we evaluate the accuracy of lagged friction models in comparison with implicit frictional contact systems. We show that major inaccuracies near the stick-slip threshold in such systems are caused by lagging of friction forces rather than by smoothing the Coulomb friction curve. Furthermore, we demonstrate how systems involving implicit or lagged friction can be correctly used with higher-order time integration and highlight limitations in earlier attempts. We demonstrate how to exploit forward-mode automatic differentiation to simplify and, in some cases, improve the performance of the inexact Newton method. Finally, we show that other complex phenomena can also be simulated effectively while maintaining smoothness of the entire system. We extend our method to exhibit stick-slip frictional behavior and preserve volume on compressible and nearly-incompressible media using soft constraints.

翻译：带摩擦接触的动力学仿真在从布料模拟到物体操控的广泛应用中具有重要意义。近期采用平滑滞后摩擦力的方法实现了带摩擦的弹性动力学鲁棒可微仿真。然而，所得摩擦行为可能不够精确，且可能无法收敛至解析解。本文评估了滞后摩擦模型相较于隐式摩擦接触系统的准确性。研究表明，此类系统在粘滑阈值附近的主要误差源于摩擦力的滞后效应，而非库仑摩擦曲线的平滑化处理。此外，我们论证了如何将涉及隐式或滞后摩擦的系统正确应用于高阶时间积分，并指出早期尝试的局限性。通过利用前向模式自动微分，我们展示了如何简化并在某些情况下提升非精确牛顿法的性能。最后，我们证明其他复杂现象亦可在保持系统整体平滑性的前提下进行有效仿真。通过引入软约束，我们将方法扩展至粘滑摩擦行为的模拟，并在可压缩与近不可压缩介质中实现了体积守恒。