Continuum modelling of viscoelastic behavior under squeezing solicitations of electrorheological fluid

In this paper, we propose a continuous model for the electromechanical behavior of the electrorheological fluids in solid state subjected to oscillatory squeeze loads below the chains rupture yield. Our starting point was the experiment led by Vieira et al. [S.L. Vieira, M. Nakano, R. Oke, T. Nagata, Mechanical properties of an ER fluid in tensile, compression and oscillatory squeeze tests, Int. J. Mod. Phys. B 15 (2001) 714-722] and the description of continua whom electromechanical properties were developed, among others, by Eringen and Maugin [G.A. Maugin, A.C. Eringen, On the equations of the electrodynamics of deformable bodies of finite extent, J. Méc. 16 (1977) 101-147; A.C. Eringen, G.A. Maugin, Electrodynamics of Continua, I: Foundations and Solid Media, Springer-Verlag, New York, 1990]. This work has been limited to small mechanical and electric perturbations of a dielectric solid free of mobile electric charges and magnetic phenomena. Similarly to works done for small thermal and mechanical perturbations in thermoelasticity, we suppose that the mechanical behavior is not coupled with the electric one. The dissipative phenomena which are experimentally observed, are modeled by an internal variable which represents the chains microscopic deformation. We present a finite element resolution to our problem, based on a variational formulation using displacement, electric potential and the internal variable. We identify our model from the inverse analysis of Vieira's tests simulation. Next, we simulate the influence of a small perturbation of the electric field on the mechanical response of the material.