# Existence for accreting viscoelastic solids at large strains

## TL;DR

This paper establishes the existence of solutions for a model describing the growth of viscoelastic solids at large strains, incorporating boundary accretion, incompatible strains, and a regularization approach.

## Contribution

It introduces a novel existence proof for a coupled accretion and viscoelastic equilibrium model with large strains and boundary growth.

## Key findings

- Existence of solutions for the accreting viscoelastic solid model.
- Regularization via a fictitious surrounding material ensures well-posedness.
- Model captures growth driven by deformation and incompatible strains.

## Abstract

By revisiting a model proposed in [45], we address the accretive growth of a viscoelastic solid at large strains. The accreted material is assumed to accumulate at the boundary of the body in an unstressed state. The growth process is driven by the deformation state of the solid. The progressive build-up of incompatible strains in the material is modeled by considering an additional backstrain. The model is regularized by postulating the presence of a fictitious compliant material surrounding the accreting body. We show the existence of solutions to the coupled accretion and viscoelastic equilibrium problem.