2D Frictional Self-Contact*

In this lecture, we implement 2D friction based on our 2D self-contact implementation in Case Study: 2D Self-Contact. The executable Python project for this section can be found at https://github.com/phys-sim-book/solid-sim-tutorial.

For simplicity, we will focus on implementing a semi-implicit version of friction. This means the normal force magnitude $\lambda$ and the tangent operator $T$ will be discretized to the last time step, and we solve the optimization once per time step without further fixed-point iterations that converge to solutions with fully-implicit friction (Frictional Contact) under the 8_self_friction folder. MUDA GPU implementations can be found at https://github.com/phys-sim-book/solid-sim-tutorial-gpu under the simulators/8_self_friction folder. Combined with the smoothly approximated static-dynamic friction transition in IPC, implementing friction into an optimization time integration framework is as straightforward as adding an extra potential energy.