This work concerns the simulation of viscoelastic behavior of polymer at different states. Viscoelastic modeling of polymer was performed from the solid state to the liquid state via a multiphase approach which is largely used to deal with the fluid structure interaction. To ensure the appreciation of the FSI, viscoelasticity is considered in two parts: an elastic one and viscous other where the main idea is to use a mixed formulation in three fields (u, v, p) (displacement, velocity, pressure), with u and v, represented the primary variables of a strain and a strain rate formulation. We are led to the Navier-Stokes compressible problem with extra-stress, which is solved by using the Mixed Finite Element. The present work contributes some stabilization elements to the numerical simulation of multiphase problem by the monolithic approach.Comparison between the literature and experiments was performed through the validation of an elastic case and the viscoelastic Kelvin-Voigt model in the context of Lagrangian framework as well as Eulerian framework. The extension of the methodology to a visco-hyper-elastic is given through the modeling and validation on material point on the finite elements library CimLib®. Finally, a stabilization scheme of the EVSS type is adopted for viscoelastic Kelvin-Voigt model, hyper-elastic Neo-Hookean model, and also visco-hyper-elastic model which proposed an open door in computational modeling, not only with viscoelasticity but also complex dynamic application.
