Abstract

A nonlinear spectral formulation, which is more general than the traditional classical-invariant formulation, is used to describe the mechanical behaviour of a residually stressed electro-elastic body with two preferred directions (ESTPD); the generality of the spectral formulation could facilitate the quest for good constitutive equations for ESTPDs. The strain energy is a function of spectral invariants (each with a clear physical meaning) that depend on the right stretch tensor, the residual stress tensor, two preferred-direction-structural tensors and one of the electric variables; clear meaningful physical invariants are useful in aiding the design of a rigorous experiment to construct a specific form of constitutive equation. Separable finite strain constitutive equations containing general single-variable functions, which depend only on a principal stretch or the electric field, are proposed and, in view of this, the corresponding infinitesimal strain energy functions can be easily constructed. A specific form for the strain energy function is generally easier to obtain from the general strain energy function via experiment if it is expressed in terms of general single-variable functions. The proposed constitutive equations can be easily converted to allow the mechanical influence of compressed fibres to be excluded or partially excluded and to model fibre dispersion in collagenous soft tissues. With the aid of spectral invariants, we easily prove that at most 15 of the 98 classical invariants in the corresponding minimal integrity basis are independent; this proof cannot be found in the literature. A simple tension boundary value problem with cylindrical symmetry is studied, where the residual stress is assumed to depend only on the radial position.