Elastic wave propagation in magneto-active fibre composites

Fibre-reinforced elastomers are lightweight and strong materials that can sustain large deformations. When filled with magnetic particles, their effective mechanical response can be modified by an external magnetic field. In the present study, we propose an effective theory of fibre-reinforced composite, based on a neo-Hookean elastic response and a linear magnetic law in each phase. The theory is shown suitable to describe the motion of composite cylinders. Furthermore, it is found appropriate for the modelling of fibre-reinforced composites subjected to a permanent magnetic field aligned with the fibres. To reach this result, we use the incremental theory (‘small on large’), in combination with homogenisation theory and the Bloch–Floquet method. This way, we show that wave directivity is sensitive to the application of a permanent magnetic field, whereas the frequency range in which wave propagation is forbidden is not modified by such a load (the band gaps are invariant). In passing, we describe a method to deduce the total stress in the material based on the measurement of two wave speeds. Furthermore, we propose an effective energy function for the description of nonlinear composites made of Yeoh-type generalised neo-Hookean fibres within a neo-Hookean matrix.