Modelling and simulation of the curing process of polymers by a modified formulation of the Arruda–Boyce model

Abstract

A phenomenologically motivated small strain model and a finite strain general framework to simulate the curing process of polymer have been developed and discussed in our recently published papers [1, 2, 3, 4]. In order to illustrate the capability of the finite strain framework proposed earlier, only the micromechanically-inspired 21-chain model and the phenomenologically motivated Neo-Hookean model (energy function) have been demonstrated so far. The Arruda–Boyce model (well-known as the 8-chain model in the elastic case and Bergstrom–Boyce model [5, 14] in the viscoelastic case) is a prototype hyperelastic model for polymeric materials. This follow-up contribution presents an extension of the Arruda–Boyce model [6] towards modelling the curing process of polymers. The necessary details, i.e. the stress tensor and the tangent operator, for the numerical implementation within the finite element method, are derived. The curing process of polymers is a complicated process where a series of chemical reactions have been activated, which will convert low molecular weight monomer solutions into more or less cross-linked solid macromolecular structures via the chemical conversion. This paper will model the elastic behaviour and shrinkage effects of the polymer curing process in the isothermal case using the Arruda–Boyce model. Several numerical examples have been demonstrated to verify our newly proposed, modified approach in case of curing process.