Mathematical analysis of successive linear approximation for Mooney-Rivlin material model in finite elasticity

TL;DR

This paper analyzes a successive linear approximation method for large deformation problems in finite elasticity, specifically for Mooney-Rivlin materials, proving the existence and uniqueness of solutions at each step.

Contribution

It introduces a mathematical framework for successive linear approximation in finite elasticity and proves solution properties for nearly incompressible Mooney-Rivlin materials.

Findings

Existence of weak solutions is established.

Uniqueness of solutions is proven.

Method is applicable to boundary value problems in finite elasticity.

Abstract

For calculating large deformations in finite elasticity, we have proposed a method of successive linear approximation, by considering the relative descriptional formulation. In this article we briefly describe this method and we prove the existence and uniqueness of weak solutions for boundary value problems for nearly incompressible Mooney-Rivlin materials, that arise in each step of the method.