A Hyperelasto-Visco-Hysteresis model for an elastomeric behaviour: Experimental and numerical investigations

The aim of this study is to investigate the mechanical behaviour of a fluoro-elastomer. Several tension and compression cyclic loading and relaxation tests have been performed to examine the nonlinear stress–strain behaviour, the loading rate-dependent response, and hysteresis phenomena during cyclic tests of this material.An original phenomenological model, named Hyperelasto-Visco-Hysteresis (HVH model), is also presented. This model, implemented in an in-house code HEREZH++, is based on the superimposition of three stress components corresponding to a linear viscoelastic, a hyperelastic and a pure hysteresis behaviour. The viscosity is described with two linear Maxwell elements which appear to be sufficient to adequately represent the viscoelastic behaviour. The hysteretic contribution of the deviatoric part of the stress tensor models the rate-independent irreversibilities of the mechanical behaviour. Contrary to other studies performed with this kind of model [1] and [2], the hyperelastic contribution is herein simulated with the Hart-Smith strain energy density function, depending only on strain invariants. The parameters of the constitutive functions are determined from the experimental data by an identification process employing nonlinear optimisation methods. The viscoelastic stress response of the rubber at large strains in relaxation and cyclic loading in compression and traction was finally compared with experimental data.