Total Lagrangian Finite Element Formulation of the Flory-Rehner Free Energy Function

TL;DR

This paper develops a comprehensive finite element implementation of the Flory-Rehner free-energy function within a hyperelastic material model, providing explicit equations and validation through numerical examples.

Contribution

It offers the first detailed derivation of the algorithmic tangent modulus for the Flory-Rehner model in a total Lagrangian finite element framework.

Findings

Validated implementation with boundary-value problems

Derived explicit equations for nonlinear analysis

Demonstrated accuracy through numerical results

Abstract

We address the total Lagrangian finite element implementation of the Flory-Rehner free-energy function in the framework of a hyperelastic material model. We explicitly give all the equations required to implement this material model in an implicit nonlinear finite element analysis, particularly, we show how to derive the so-called algorithmic or consistent linearized tangent modulus in the Lagrangian description. Some analytical and numerical results for different boundary-value problems are presented to validate the implementation.