Codimensional incremental potential contact

We extend the incremental potential contact (IPC) model [Li et al. 2020a] for contacting elastodynamics to resolve systems composed of codimensional degrees-of-freedoms in arbitrary combination. This enables a unified, interpenetration-free, robust, and stable simulation framework that couples codimension-0,1,2, and 3 geometries seamlessly with frictional contact. Extending the IPC model to thin structures poses new challenges in computing strain, modeling thickness and determining collisions. To address these challenges we propose three corresponding contributions. First, we introduce a C2 constitutive barrier model that directly enforces strain limiting as an energy potential while preserving rest state. This provides energetically-consistent strain limiting models (both isotropic and anisotropic) for cloth that enable strict satisfaction of strain-limit inequalities with direct coupling to both elastodynamics and contact via minimization of the incremental potential. Second, to capture the geometric thickness of codimensional domains we extend the IPC model to directly enforce distance offsets. Our treatment imposes a strict guarantee that mid-surfaces (respectively mid-lines) of shells (respectively rods) will not move closer than applied thickness values, even as these thicknesses become characteristically small. This enables us to account for thickness in the contact behavior of codimensional structures and so robustly capture challenging contacting geometries; a number of which, to our knowledge, have not been simulated before. Third, codimensional models, especially with modeled thickness, mandate strict accuracy requirements that pose a severe challenge to all existing continuous collision detection (CCD) methods. To address these limitations we develop a new, efficient, simple-to-implement additive CCD (ACCD) method that applies conservative advancement [Mirtich 1996; Zhang et al. 2006] to iteratively refine a lower bound for deforming primitives, converging to time of impact. In combination these contributions enable codimensional IPC (C-IPC). We perform extensive benchmark experiments to validate the efficacy of our method in capturing intricate behaviors of thin-structure contact and resulting bulk effects. In our experiments C-IPC obtains feasible, convergent, and so artifact-free solutions for all time steps, across all tested examples - producing robust simulations. We test C-IPC across extreme deformations, large time steps, and exceedingly close contact over all possible pairings of codimensional domains. Finally, with our strain-limit model, we confirm C-IPC guarantees non-intersection and strain-limit satisfaction for all reasonable (and well below - verified down to 0.1%) strain limits throughout all time steps.