Incremental potential contact

Abstract

Contacts weave through every aspect of our physical world, from daily household chores to acts of nature. Modeling and predictive computation of these phenomena for solid mechanics is important to every discipline concerned with the motion of mechanical systems, including engineering and animation. Nevertheless, efficiently time-stepping accurate and consistent simulations of real-world contacting elastica remains an outstanding computational challenge. To model the complex interaction of deforming solids in contact we propose Incremental Potential Contact (IPC) - a new model and algorithm for variationally solving implicitly time-stepped nonlinear elastodynamics. IPC maintains an intersection- and inversion-free trajectory regardless of material parameters, time step sizes, impact velocities, severity of deformation, or boundary conditions enforced. Constructed with a custom nonlinear solver, IPC enables efficient resolution of time-stepping problems with separate, user-exposed accuracy tolerances that allow independent specification of the physical accuracy of the dynamics and the geometric accuracy of surface-to-surface conformation. This enables users to decouple, as needed per application, desired accuracies for a simulation's dynamics and geometry. The resulting time stepper solves contact problems that are intersection-free (and thus robust), inversion-free, efficient (at speeds comparable to or faster than available methods that lack both convergence and feasibility), and accurate (solved to user-specified accuracies). To our knowledge this is the first implicit time-stepping method, across both the engineering and graphics literature that can consistently enforce these guarantees as we vary simulation parameters. In an extensive comparison of available simulation methods, research libraries and commercial codes we confirm that available engineering and computer graphics methods, while each succeeding admirably in custom-tuned regimes, often fail with instabilities, egregious constraint violations and/or inaccurate and implausible solutions, as we vary input materials, contact numbers and time step. We also exercise IPC across a wide range of existing and new benchmark tests and demonstrate its accurate solution over a broad sweep of reasonable time-step sizes and beyond (up to h = 2s) across challenging large-deformation, large-contact stress-test scenarios with meshes composed of up to 2.3M tetrahedra and processing up to 498K contacts per time step. For applications requiring high-accuracy we demonstrate tight convergence on all measures. While, for applications requiring lower accuracies, e.g. animation, we confirm IPC can ensure feasibility and plausibility even when specified tolerances are lowered for efficiency.

Discrete element model for general polyhedra

“…Note that a given input of ζ does not necessarily represent the classical behavior of a mass-spring-dashpot model (for example ζ = 1 leading to a critical damping ratio). Indeed, the viscous damping can change when expressed by (53). Moreover, in the present context we may have multiple simultaneous contact forces between bodies.…”

Inversion-free geometric mapping construction: A survey

“…In addition to being inversion-free, applications may ask for intersection-free boundaries [13,32,84,85]. An inversion-free and intersection-free mapping is bijective.…”

“…In 3D, when two boundary edges are close to each other, they will collide. For the first question, the distance from a boundary vertex to a boundary element or the distance between two boundary edges is used, denoted as d inter [32,85].…”

“…The barrier functions are at least C 2 when d inter < inter . Thus quasi-Newton solvers [32] and second-order solvers [13,85] can be used. However, the number of potential collisions is quadratic in the number of boundary elements, and thus the density of the Hessian matrix in secondorder solvers significantly increases, thereby causing much more time for optimization.…”

Rapidly encoding generalizable dynamics in a Euclidean symmetric neural network: a Slinky case study

“…The ESNN will be frozen after training. A damping and a contact model [39] will be added in the NN deployment to match the real-world energy dissipation and non-penetration. The ESNN is trained on this one case, and tested for other cases with different boundary conditions, Slinky orientation, and number of cycles.…”