<p>In this communication, we develop a nonlinear spectral invariant-based framework for modelling the electrical behaviour of stiff fibre-reinforced composites. Within the couple-stress theory, we construct general constitutive equations for stress and couple stress that capture the interactions between mechanical and electrical fields. To model materials in which resistance to fibre bending plays a dominant role, we refine the general constitutive equations by restricting their dependence on the fibre direction gradient to the directional derivative along the fibre axis. Prototype forms of the internal energy function are proposed for both the general and specialized cases. We demonstrate the applicability of the specialized model by solving boundary value problems involving fibre bending and inflation, highlighting its physical relevance. Our results provide a basis for the design and simulation of advanced smart materials, particularly in contexts where electrical effects and fibre microstructure are strongly coupled.</p>