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 β. 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. .
