Application of the Virtual Fields Method to a relaxation behaviour of rubbers

This paper presents the application of the Virtual Fields Method (VFM) for the characterization of viscoelastic behaviour of rubbers. The relaxation behaviour of the rubbers following a dynamic loading event is characterized using the dynamic VFM in which full-field (two dimensional) strain and acceleration data, obtained from high-speed imaging, are analysed by the principle of virtual work without traction force data, instead using the acceleration fields in the specimen to provide stress information. Two (silicone and nitrile) rubbers were tested in tension using a drop-weight apparatus. It is assumed that the dynamic behaviour is described by the combination of hyperelastic and Prony series models. A VFM based procedure is designed and used to produce the identification of the modulus term of a hyperelastic model and the Prony series parameters within a time scale determined by two experimental factors: imaging speed and loading duration. Then, the time range of the data is extended using experiments at different temperatures combined with the time-temperature superposition principle. Prior to these experimental analyses, finite element simulations were performed to validate the application of the proposed VFM analysis. Therefore, for the first time, it has been possible to identify relaxation behaviour of a material following dynamic loading, using a technique that can be applied to both small and large deformations.