# Quasistatic viscoelasticity with self-contact at large strains

## TL;DR

This paper develops a mathematical framework for large-strain quasistatic viscoelasticity with self-contact, ensuring the existence of weak solutions that are almost everywhere injective, using a Lagrangian approach and 2nd-grade nonsimple materials.

## Contribution

It introduces a novel formulation of Kelvin-Voigt viscoelasticity at large strains with self-contact in the reference configuration, proving existence of weak solutions.

## Key findings

- Existence of weak solutions with a.e. injectivity.
- Framework accommodates self-contact in large strains.
- Uses implicit time discretisation for convergence.

## Abstract

The frame-indifferent viscoelasticity in Kelvin-Voigt rheology at large strains is formulated in the reference configuration (i.e. using the Lagrangian approach) considering also the possible self-contact in the actual deformed configuration. Using the concept of 2nd-grade nonsimple materials, existence of certain weak solutions which are a.e. injective is shown by converging an approximate solution obtained by the implicit time discretisation.