Fully implicit frictional dynamics with soft constraints

Dynamics simulation with frictional contacts is important for a wide range of applications, from cloth simulation to object manipulation. Recent methods using smoothed friction forces have enabled robust and differentiable simulation of elastodynamics with friction. However, the resulting frictional behaviors can be qualitatively inaccurate and may not converge to analytic solutions. Here we propose an alternative, fully implicit, formulation for simulating elastodynamics subject to frictional contacts with realistic friction behavior. Furthermore, we demonstrate how higher-order time integration can be used in our method, as well as in incremental potential methods. We develop an inexact Newton method with forward-mode automatic differentiation that simplifies the implementation and improves performance. Finally, we show how our method can be extended to respond to volume changes using a unified penalty function derived from first principles and capable of emulating compressible as well as nearly incompressible media.