Thermodynamic consistent modeling of polymer curing coupled to visco–elasticity at large strains

Abstract

We develop a macroscopic constitutive model for temperature-dependent visco–elastic effects accompanied by curing, which are important phenomena in production processes. Within a thermodynamic framework we use an additive ternary decomposition of the logarithmic Hencky strain tensor into mechanical, thermal and chemical parts. Based on the concept of stoichiometric mass fractions for resin, curing agent and solidified material the bulk compression modulus as well as the bulk heat- and shrinking dilatation coefficients are derived and compared with ad hoc assumptions from the literature. Moreover, we use the amount of heat generated during differential scanning calorimetry until completion of the chemical reactions, to define the chemical energy. As a major result, the resulting latent heat of curing occurring in the heat-conduction equation derived in our approach reveals an ad hoc approach from the literature as a special case. In addition, thermodynamic consistency of the model will be proved, and the numerical implementation of the constitutive equations into a finite-element program is described. In the examples we illustrate the characteristic behaviour of the model, such as shrinking due to curing and temperature dependence and simulate the deep drawing of a spherical part with the finite-element-method.