The incremental Virtual Fields Method and pre-stretching method applied to rubbers under uniaxial medium-strain-rate loading

Conventional dynamic experiments on rubbers have several limitations including low signal-to-noise ratio and a long time period during which the specimen is not in static equilibrium, which causes difficulties separating constitutive material behaviour from specimen response. In order to overcome these limitations, the present study builds on previous research in which the Virtual Fields Method (VFM) is applied to dynamic tensile experiments. A previous study has demonstrated that the VFM can be used to identify the material parameters of a hyperelastic model for a given rubber based on optical measurements of wave propagation in the rubber, eliminating the need for force measurements by instead using acceleration fields as a ‘virtual load cell’. In order to successfully characterise the strain hardening in the material, large deformations are required, and these were achieved by applying static pre-loads to the specimen before the dynamic loading. In order to then apply the VFM, measurements of the static force, or strain, or both, are required. This paper explores different methods for applying the VFM, in particular comparing the use of a static force measurement, as in the previous research, to methods which only require strain fields in order to apply the incremental equation of motion. FEM simulations were conducted to compare the identification sensitivity to experimental error sources between the two VFM implementations; the experimental data used in the previous studies were then applied to the incremental VFM. A further experimental comparison is provided between constitutive parameters obtained in tensile experiments using the VFM and compressive measurements from a modified split Hopkinson bar technique equipped with a piezoelectric force transducer. Finally, there is a discussion of the effects of pre-loading and relaxation in the material