Quadratically nonlinear interactions of shear elastic waves in fiber-reinforced orthotropic materials

This paper investigates the interaction of weakly nonlinear waves in a hyperelastic, fiber-reinforced orthotropic material. The study focuses on quadratically nonlinear effects. Using a multiple scale asymptotic expansion, the coupled evolution equations for the amplitudes of different pairs of waves are derived. It turns out that unlike as it is in the isotropic case, the quadratically nonlinear coupling is possible between shear elastic waves. The derived coupled evolution equations for the amplitudes of interacting wave pairs offer new insights into the behavior of elastic waves in such complex material systems, contributing to the understanding of wave phenomena in fiber-reinforced materials.