On the electromagnetic Cosserat spectral modelling of fibre-reinforced composites with fibre bending stiffness

Abstract

In this study, we develop a nonlinear framework based on spectral invariants to model the electromagnetic behaviour of fibre-reinforced composites, explicitly accounting for the fibre stiffness of the embedded fibres. Employing Cosserat continuum theory, we derive general constitutive equations for stress and couple stress that capture the interactions between mechanical and electromagnetic fields. These equations also enable a physically meaningful decomposition of the couple stress tensor. To model materials in which fibre bending plays a dominant role, we refine the general constitutive equations by restricting their dependence on fibre direction gradients to directional derivatives 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. The results offer a foundation for the design and simulation of advanced smart materials, particularly in applications where electromagnetic effects and fibre microstructure are strongly coupled.