Identifying hyperelastic constitutive parameters with sensitivity-based virtual fields

This work deals with the identification of hyperelastic constitutive parameters using the virtual fields method. The choice of the virtual displacement fields is a crucial aspect of the method, typically for reducing the sensitivity to the measurement noise. A first and simple option is to generate the virtual displacement fields randomly. Nevertheless, in case of hyperelastic models for which the stress is not a linear function of the constitutive parameters, improving the choice of the virtual displacement fields is not trivial and an alternative strategy has to be found. In the present study, the sensitivity-based virtual fields approach is applied and compared with the randomly generated virtual displacement fields approach. Two material models were considered: the Mooney model, which describes quite well the behavior of hyperelastic materials for small and moderate strains, and the Ogden model, which accounts for the stress hardening phenomenon observed at higher strains. The full kinematic fields are measured by using the digital image correlation technique during an equibiaxial tensile test performed on a cruciform specimen. Identification results are discussed through their capability to predict the external force measured during the test. The sensitivity-based virtual fields approach is found to improve significantly the prediction compared with the randomly generated virtual displacement fields approach.