On 2D Viscoelasticity with Small Strain

TL;DR

This paper develops an exact 2D model for incompressible viscoelastic materials using polar decomposition, proving global existence of solutions under small initial strains by leveraging weak dissipation mechanisms.

Contribution

It introduces a novel 2D rotation-strain model for viscoelasticity and establishes global existence results based on weak dissipation, advancing theoretical understanding.

Findings

Global existence of classical solutions proved for small initial strains.

The model accurately describes the motion of incompressible viscoelastic materials.

Weak dissipation is key to the proof of global solutions.

Abstract

An exact two-dimensional rotation-strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under the smallness assumptions only on the size of initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, which is revealed by passing the partial dissipation to the whole system.