  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.
