The secular equation for non-principal Rayleigh waves in deformed incompressible doubly fiber-reinforced nonlinearly elastic solids

• Explicit and implicit secular equations for the speed of a Rayleigh wave in a pre-stressed, anisotropic half-space are obtained.
• The anisotropy is associated with two preferred directions, thereby modeling the effect of two families of fiber reinforcement.
• Results are illustrated with numerical examples.
• The wave speed depends strongly on the anisotropic character of the material model.

The explicit and implicit secular equations for the speed of a (surface) Rayleigh wave propagating in a pre-stressed, doubly fiber-reinforced incompressible nonlinearly elastic half-space are obtained. Hence, the anisotropy is associated with two preferred directions, thereby modelling the effect of two families of fiber reinforcement. One of the principal planes of the primary pure homogeneous strain coincides with the free surface while the surface wave is not restricted to propagate in a principal direction. Results are illustrated with numerical examples. In particular, an isotropic material reinforced with two families of fibers is considered. Each family of fibers is characterized by defining a privileged direction. Furthermore, the fibers of each family are located throughout the half space and run parallel to each other and perpendicular to the depth direction, i.e. the free surface is a plane of symmetry of the anisotropy. The wave speed depends strongly on the anisotropic character of the material model as well as the direction of propagation.