On the phenomenological representation of curing phenomena in continuum mechanics

Abstract

To simulate curing phenomena, for example for the purpose of optimising the manufacturing processes or to calculate the stress distribution in adhesive seams, constitutive models representing the thermomechanically-coupled behaviour of adhesives are required. During the curing reaction, the adhesive changes its thermomechanical material behaviour from a viscous fluid to a viscoelastic solid. This phase transition is an exothermal chemical reaction which is accompanied by thermal expansion, chemical shrinkage and changes in temperature. In this essay we develop a physically-based theory of finite strain thermoviscoelasticity to represent these phenomena. To this end, we introduce a multiplicative split of the deformation gradient into a thermal, a chemical and a mechanical part. We define the coordinate of chemical reaction determined by an evolution equation to describe the temporal behaviour of the curing reaction. The free energy of the model contains an additional term, the chemically-stored free energy, which depends on this internal variable. The mechanical behaviour of the adhesive is modelled using a constitutive approach of finite thermoviscoelasticity and the viscosities are functions of the coordinate of chemical reaction. We show that the model is compatible with the Clausius–Duhem inequality, derive the equation of heat conduction and illustrate the physical properties of the theory by a numerical example.