Constitutive relation and electromechanical stability of compressible dielectric elastomer

The constitutive relation and electromechanical stability of Varga-Blatz-Ko-type compressible isotropic dielectric elastomer is investigated in this paper. Free-energy in any form, which consists of elastic strain energy and electric energy, can be applied to analyse the electromechanical stability of dielectric elastomer. The constitutive relation and stability is analyzed by applying a new kind of free energy model, which couples elastic strain energy, composed of Varga model as the volume conservative energy and Blatz-Ko model as the volume non-conservative energy, and electric field energy with constant permittivity. The ratio between principal planar stretches m(t 0 ) (λ 2 = m(t 0 )λ 1 ), the ratio between thickness direction stretch and length direction stretch 0 n(t 0 ) (λ 3 = n(t 0 )λ 1 ), and power exponent of the stretch k(t 0 ) are defined to characterize the mechanical loading process and compressible behavior of dielectric elastomer. Along with the increase of material parameters m(t 0 ) , n(t 0 ) , k(t 0 ) and poison ratio V , the nominal electric field peak is higher. This indicates that the dielectric elastomer electromechanical system is more stable. Inversely, with the increase of the material parameter α , the nominal electric field peak, critical area strain and the critical thickness strain increase, coupling system is more stable.