A new frame for constitutive modeling of visco elastic polymers; Accounting thermal effects and strain induced crystallization
Résumé
Modelling the mechanical behaviour of polymers is a nontrivial task. Usual macroscopic approaches that decompose global deformation into three elementary components in a "a priori" manner often results in complex and "of limited efficiency" models. This study deals at promoting another concept of visco-hyper-elasticity for polymers close to Tg without arbitrary decomposition into "viscous" and "elastic" stresses or strains. To achieve that point, a hyper elastic model is extended to account for inelastic processes. Those latter are assumed to result in a kinetics of variation of internal variables that have to be accounted for in the energy balance at any time and that induce time effects in the writing. Variables of interest are related to de entanglement and/or strain induced crystallisation through specific kinetics laws. This version uses Edward-Vilgis' network theory that depends on four physical parameters: the density of fixed network nodes, the density of sliding nodes or entanglements, a parameter ultimately related to chain extensibility and a parameter ultimately representative for level of freedom of entanglements. The stress is written in the framework of Irreversible Processes Thermodynamics (IPT) and in the frame of large strain approximations. Mechanical problem is coupled to thermal problem using Taylor-Quinney coefficient ß. Equations are included in a finite difference code (using a-method) to calculate temperature and stress through the central section of a sample. Parameters identification is based on the minimisation of a two objectives cost function that accounted for average axial stress in the section and for surface temperature at this section. This latter was written in a mean-square approach.