On Spectral Couple Total-Stress Modelling of Stiff Fibre-Reinforced Electroactive Viscoelastic Composites

Abstract We present a nonlinear spectral invariant–based framework for modeling the electromechanical behavior of viscoelastic stiff fibre-reinforced electro-active composites. Within a couple-stress theory, we derive general constitutive equations for the total stress and total couple-stress that capture the coupling between mechanical and electrical fields. To model materials in which resistance to fibre bending is dominant, the constitutive equations are specialized by restricting their dependence on the gradient of the fibre direction to the directional derivative along the fibre axis. The resulting constitutive models are expressed in terms of spectral invariants, each of which admits a clearer physical interpretation than classical invariants. This feature makes the models particularly suitable for experimental identification using systematic curve-fitting procedures for the free-energy function. The number of complete, irreducible, and minimal spectral invariants is significantly smaller than that of the classical complete-irreducible invariants reported in the literature, leading to a substantial reduction in modelling complexity. The applicability of the specialized model is illustrated through boundary-value problems involving fibre bending and inflation, highlighting its relevance for experimental and applied settings. The proposed framework provides a rigorous basis for the modeling and simulation of viscoelastic electro-active materials with strongly coupled fibre microstructure.