Asynchronous Variational Integration of Interaction Potentials for Contact Mechanics

TL;DR

This paper extends the theoretical foundation of Asynchronous Variational Integrators (AVIs) to include interaction potentials, enabling accurate long-term simulations of contact mechanics without energy drift.

Contribution

It proves that AVIs remain multisymplectic with interaction potentials, broadening their applicability to contact mechanics and multibody systems.

Findings

AVIs maintain multisymplecticity with interaction potentials

Long-term energy behavior is stable in contact simulations

Comparison shows improved energy conservation over existing methods

Abstract

Asynchronous Variational Integrators (AVIs) have demonstrated long-time good energy behavior. It was previously conjectured that this remarkable property is due to their geometric nature: they preserve a discrete multisymplectic form. Previous proofs of AVIs' multisymplecticity assume that the potentials are of an elastic type, i.e., specified by volume integration over the material domain, an assumption violated by interaction-type potentials, such as penalty forces used to model mechanical contact. We extend the proof of AVI multisymplecticity, showing that AVIs remain multisymplectic under relaxed assumptions on the type of potential. The extended theory thus accommodates the simulation of mechanical contact in elastica (such as thin shells) and multibody systems (such as granular materials) with no drift of conserved quantities (energy, momentum) over long run times, using the algorithms in [3]. We present data from a numerical experiment measuring the long time energy behavior of simulated contact, comparing the method built on multisymplectic integration of interaction potentials to recently proposed methods for thin shell contact.