Inertial evolution of non-linear viscoelastic solids in the face of (self-)collision

TL;DR

This paper proves the existence of weak solutions for the complex problem of inertial, non-linear viscoelastic solids undergoing contact and collision, including measure-valued contact forces, conserving momentum and energy.

Contribution

It provides a rigorous mathematical proof of weak solutions for non-linear viscoelastic solids with contact, addressing an open problem in the field.

Findings

Existence of weak solutions for arbitrary times and initial data

Inclusion of measure-valued contact forces obeying physical laws

A new compactness result for contact forces

Abstract

We study the time evolution of non-linear viscoelastic solids in the presence of inertia and (self-)contact. For this problem we prove the existence of weak solutions for arbitrary times and initial data, thereby solving an open problem in the field. Our construction directly includes the physically correct, measure-valued contact forces and thus obeys conservation of momentum and an energy balance. In particular, we prove an independently useful compactness result for contact forces.