The Ogden and the extended tube model as backbone in describing electroactive polymers: advancements in modelling nonlinear behaviour and fracture.

Hyperelastic constitutive relations form the basis of advanced models for novel materials. Such elastic deformation potentials are the backbone for complex material formulations at elastic and inelastic deformations, especially when embedded into powerful frameworks like generalized standard materials, as well as multiphysical and multiscale formulations. With the focus on electroactive polymers, the article at hand demonstrates the derivation of a variational, rate-dependent electromechanical model for quasi-incompressible polymers and the derivation of an electromechanical model for regularized fracture mechanics by means of the phase-field method. Starting at the prominent Ogden and the extended tube model, some developments from the last decades are revisited and presented via the principle of virtual power, for instance, the established mixed element formulation, nonlinear viscoelasticity and electromechanical coupling. An electromechanically fully coupled representative crack element is used to derive a novel phase-field model for fracture. A key property of the proposed model is the ability to describe the electrical free-space behaviour inside the crack gap, which is demonstrated by adopting three common crack-face conditions. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.