Continuum Physics of Materials with Time-Dependent Properties: Reviewing the Case of Polymer Curing

A temporal evolution of material parameters may appear in many fields; as a paradigm the curing process of polymeric materials is here considered. Thereby, a systematic overview is presented in this contribution whereby modeling various aspects of the polymer curing process under different types of loads are investigated. Physically based, small and finite strain curing models have been developed that can work under a purely mechanical load where the time dependence of the material parameters appearing in the models are considered. The curing process of polymers under a purely mechanical load 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. To work under various classes of coupled loads, e.g., thermomechanical, magnetomechanical, and electromechanical loads, the initially developed modeling framework suited for a mechanical load is extended. Thereby, capturing the curing process in the presence of a magnetomechanical or an electromechanical load becomes even more challenging. In the current contribution, thermodynamically consistent small and finite strain constitutive frameworks are revisited which are based either on a direct time-dependent formulation or on a degree of cure-dependent formulation. The degree of cure is a key parameter in the curing (reaction) kinetics. Both our mechanical and several coupled modeling frameworks are in line with a rate-type hypoelastic approach. Some representative numerical examples are discussed under various forms of mechanical and nonmechanical loads which show the capability of different constitutive formulations to capture major phenomena observed during the curing process of polymers.