Constitutive models for anisotropic dielectric elastomer composites: Finite deformation response and instabilities

Abstract

This paper is concerned with the generation of homogenization estimates for electroelastic composites consisting of initially aligned, rigid dielectric fibers that are distributed with random positions in a dielectric elastomeric matrix. For this purpose, use is made of a certain “partial decoupling strategy” resulting in the splitting of the macroscopic energy of the composite into a purely mechanical and a purely electrostatic component—coupled only by the average rotation of the fibers. In addition to the macroscopic electro-mechanical constitutive response for the composite, the procedure delivers estimates for the average fiber rotation as a consequence of the combined action of the mechanical stresses and electrical torques under general in-plane loading conditions. It is found that when large compressive stresses are applied along the long axes of the fibers, the composite may undergo a “macroscopic” (i.e., material) instability that is captured by loss of ellipticity of the overall incremental response and corresponds to spontaneous rotation of the fibers to relieve the large stresses. Moreover, when the electric field is aligned with the long axes of the fibers, it tends to stabilize the response, while when it is transverse to them, it tends to destabilize the response. Earlier estimates obtained by means of a simplifying “partial decoupling approximation” are compared with the new, more robust estimates and found to become less accurate with increasing electric field magnitudes.