Extremal states and coupling properties in electroelasticity

Electroelastic materials possess properties most attractive for the design of smart devices and systems such as actuators and sensors. Typical polymers show changes in shape under the action of an electric field, and vice versa, together with fast actuation times, high strain levels and low elastic moduli. This paper deals with an Ogden model inspired framework for large deformation electroelasticity which, as a special case, can also be reduced to the modelling of transversely isotropic elasticity. Extremal (local) states are elaborated based on a coaxiality analysis, i.e. extremal states of energy are considered at fixed deformation and changing direction of electric field, respectively, fixed electric field and changing principal directions of deformation. This analysis results in extremal states when stresses and strain commutate, respectively, dielectric displacements and electric field are aligned. In order to further elaborate electromechanical coupling properties, the sensitivity of stresses with respect to electric field is analysed. This sensitivity is represented by a third-order tensor which, in general, depends on deformation and electric field. To illustrate this third-order tensor, a decomposition into deviators is adopted. Related norms of these deviators, together with the electromechanical coupling contribution to the augmented energy, are investigated for different states under homogeneous deformation and changing electric field direction. The analysis is considered to contribute to a better understanding of electromechanical coupling properties and extremal states in large deformation electroelasticity and by that, as a long-term goal, may contribute to the improved design of related smart devices and systems. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.