Couple stress modelling of stiff fibre-reinforced magneto viscoelastic composites

We develop a nonlinear spectral-invariant–based framework for the constitutive modelling of viscoelastic, stiff fibre-reinforced magneto-active composites. Within a couple-stress continuum formulation, general expressions for the total stress and its relation with couple stress are derived, enabling the consistent description of coupled mechanical and magnetic effects. For materials in which fibre-bending resistance dominates the energetic response, the constitutive structure is specialized by restricting the dependence on the fibre-direction gradient to its directional derivative along the fibre axis. The resulting models are formulated in terms of spectral invariants that possess clearer physical interpretation than classical invariant sets, facilitating experimental identification through systematic curve-fitting of the free-energy function. Moreover, the number of complete, irreducible, and minimal invariants required is substantially smaller than that in classical invariant bases, significantly reducing model complexity. Representative boundary-value problems involving fibre bending and inflation demonstrate the applicability of the formulation. The proposed framework provides a rigorous and efficient basis for modelling viscoelastic magneto-active composites with strongly coupled fibre microstructures.