A Non-Second-Gradient Model for Nonlinear Electroelastic Bodies with Fibre Stiffness

Abstract

The study of the mechanical behaviour of fibre-reinforced electroactive polymers (EAPs) with bending stiffness is beneficial in engineering for mechanical design and problem solving. However, constitutive models of fibre-reinforced EAPs with fibre bending stiffness do not exist in the literature. Hence, to enhance the understanding of the mechanical behaviour of fibre-reinforced EAPs with fibre bending stiffness, the development of a relevant constitutive equation is paramount. In this paper, we develop a constitutive equation for a nonlinear nonpolar EAP, reinforced by embedded fibres, in which the elastic resistance of the fibres to bending is modelled via the classical branches of continuum mechanics without using the second gradient theory, which assumes the existence of contact torques. In view of this, the proposed model is simple and somewhat more realistic, in the sense that contact torques do not exist in nonpolar EAPs.

Keywords

• fibre-reinforced electroactive polymers
• bending stiffness
• spectral invariant
• nonpolar
• hyperelasticity