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

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