Case Study: Inversion-free Elasticity*

At the end of this chapter, we implement the Neo-Hookean model introduced in the previous lectures to simulate inversion-free elastic solids. The excutable Python project for this section can be found at https://github.com/phys-sim-book/solid-sim-tutorial under the 6_inv_free folder. MUDA GPU implementations can be found at https://github.com/phys-sim-book/solid-sim-tutorial-gpu under the simulators/6_inv_free folder. Instead of discretizing elasticity onto the springs as in the mass-spring model, we discretize the Neo-Hookean model onto triangle elements, apply chain rules to compute elastic forces according to the relation between deformation gradient $\mathbf{F}$ and world-space nodal position $\mathbf{x}$, and then develop a root-finding based approach to filter the initial step size of line search for guaranteed non-inversion.