Convergent Incremental Potential Contact

TL;DR

This paper introduces a continuous formulation and discretization of the Incremental Potential Contact (IPC) model, enabling convergence under refinement for elastodynamics simulations involving frictional contact.

Contribution

It presents the first convergent discretization of IPC potentials by reformulating them in a continuous setting, improving simulation accuracy and reliability.

Findings

Demonstrates convergence behavior on elastostatic and dynamic problems

Validates accuracy against analytical benchmarks

Shows improved simulation stability and precision

Abstract

Recent advances in the simulation of frictionally contacting elastodynamics with the Incremental Potential Contact (IPC) model have enabled inversion and intersection-free simulation via the application of mollified barriers, filtered line-search, and optimization-based solvers for time integration. In its current formulation the IPC model is constructed via a discrete constraint model, replacing non-interpenetration constraints with barrier potentials on an already spatially discretized domain. However, while effective, this purely discrete formulation prohibits convergence under refinement. To enable a convergent IPC model we reformulate IPC potentials in the continuous setting and provide a first, convergent discretization thereof. We demonstrate and analyze the convergence behavior of this new model and discretization on a range of elastostatic and dynamic contact problems, and evaluate its accuracy on both analytical benchmarks and application-driven examples.