High-Order Incremental Potential Contact for Elastodynamic Simulation on Curved Meshes

High-order meshes provide a more accurate geometrical approximation of an object's boundary (where stress usually concentrates, especially in the presence of contacts) than linear elements, for a negligible additional cost when used in a finite element simulation. High-order bases provide major advantages over linear ones in terms of efficiency, as they provide (for the same physical model) higher accuracy for the same running time, and reliability, as they are less affected by locking artifacts and mesh quality. Thus, we introduce a high-order finite element formulation (high-order basis) for elastodynamic simulation on high-order (curved) meshes with contact handling based on the recently proposed Incremental Potential Contact model. Our approach is based on the observation that each IPC optimization step used to minimize the elasticity, contact, and friction potentials leads to linear trajectories even in the presence of non-linear meshes or non-linear finite element basis. It is thus possible to retain the strong non-penetration guarantees and large time steps of the original formulation while benefiting from the high-order basis and high-order geometry. Additionally, we show that collision proxies can be naturally incorporated into this formulation. We demonstrate the effectiveness of our approach in a selection of problems from graphics, computational fabrication, and scientific computing.