Closed-form and numerical stress solution-based parameter identification for incompressible hyper-viscoelastic solids subjected to various loading modes

This paper presents closed-form and numerical stress solutions for incompressible hyper-viscoelastic solids considering the following loading modes: uniaxial and equibiaxial tension/compression, pure shear and simple shear. The analytical stress solutions are based on three widely-used hyperelastic material models (Neo-Hookean, Mooney-Rivlin, Ogden model) and assume constant engineering strain rate. On the contrary, the numerical stress solutions are independent of both the hyperelastic law and the loading history. It has been confirmed that these stress solutions can be utilised to identify the hyper-viscoelastic material model parameters. In addition, the closed-form stress solutions may allow verifying different numerical time integration schemes. The accuracy of the constitutive constants extracted for an isoprene rubber has been investigated by comparing the predicted and the measured behaviour. The very good agreement between them shows clearly the benefit of the stress solutions presented.