Asynchronous Variational Contact Mechanics

TL;DR

This paper introduces an asynchronous variational integrator approach for simulating elastica with complex contact and impact, allowing different time steps for forces to improve robustness and energy conservation.

Contribution

It extends AVIs to handle contact forces with variable time stepping, ensuring momentum and energy conservation in complex impact scenarios.

Findings

Demonstrates robustness in 2D and 3D contact simulations.

Maintains good energy behavior during simulations.

Handles complex impact scenarios effectively.

Abstract

An asynchronous, variational method for simulating elastica in complex contact and impact scenarios is developed. Asynchronous Variational Integrators (AVIs) are extended to handle contact forces by associating different time steps to forces instead of to spatial elements. By discretizing a barrier potential by an infinite sum of nested quadratic potentials, these extended AVIs are used to resolve contact while obeying momentum- and energy-conservation laws. A series of two- and three-dimensional examples illustrate the robustness and good energy behavior of the method.