Degree of cure-dependent modelling for polymer curing processes at small-strain. Part I: consistent reformulation

A physically-based small strain curing model has been developed and discussed in our previous contribution (Hossain et al. in Comput Mech 43:769-779, 2009a) which was extended later for finite strain elasticity and viscoelasticity including shrinkage in Hossain et al. (Comput Mech 44(5):621-630, 2009b) and in Hossain et al. (Comput Mech 46(3):363-375, 2010), respectively. The previously proposed constitutive models for curing processes are based on the temporal evolution of the material parameters, namely the shear modulus and the relaxation time (in the case of viscoelasticity). In the current paper, a thermodynamically consistent small strain constitutive model is formulated that is directly based on the degree of cure, a key parameter in the curing (reaction) kinetics. The new formulation is also in line with the earlier proposed hypoelastic approach. The curing process of polymers is a complex phenomenon involving a series of chemical reactions which transform a viscoelastic fluid into a viscoelastic solid during which the temperature, the chemistry and the mechanics are coupled. Part I of this work will deal with an isothermal viscoelastic formulation including shrinkage effects whereas the following Part II will give emphasis on the thermomechanical coupled approach. Some representative numerical examples conclude the paper and show the capability of the newly proposed constitutive formulation to capture major phenomena observed during the curing processes of polymers.