Reformulation of the virtual fields method using the variation of elastic energy for parameter identification of \({\textbf {QR}}\) decomposition-based hyperelastic models

\({\textbf {QR}}\) decomposition-based constitutive relations for hyperelastic materials have attracted great attention from the community of solid mechanics, as hyperelastic models in terms of the distortion tensor \(\varvec{\widetilde{F}}\) have obvious physical meanings. However, there are few works systematically discussing the material parameter identification for \({\textbf {QR}}\) decomposition-based hyperelastic models. In this work, we reformulate the virtual fields method by considering the internal virtual work as the variation of elastic energy caused by virtual displacements. This approach (together with the \({\textbf {QR}}\) decompositions) is more concise and easier to be implemented when compared with the conventional approach, which requires specific stresses, such as Cauchy stress, first or second Piola–Kirchhoff stress, and conjugate virtual strains to calculate the internal virtual work. To validate the reformulated virtual fields method, we derive the Mooney–Rivlin model under the \({\textbf {QR}}\) framework, and then identify its material parameters for incompressible silicone specimens under biaxial tensile tests. The results indicate that the proposed virtual fields method works very well for \({\textbf {QR}}\) decomposition-based models.