Shear- or traction-induced motions in incompressible transversely isotropic dispersive materials

In this paper, we analyze a linearized model for incompressible transversely isotropic dispersive fiber-reinforced materials in which both the elastic and dispersive properties depend on the direction of the fibers. We investigate the motions in bodies made of these materials that are subjected to prescribed shear or normal action on part of the rigid boundaries. In the case where the motion is induced by shear stresses acting at the boundary, we provide the analytical solution for the displacement field from which we derive the components of the stress tensor. In the case where the motion is due to the action of normal stresses at the boundary, the initial and boundary value problem is solved using a projection algorithm based on spectral methods. In both cases, we quantify how anisotropic dispersion and material stiffness affect the displacement field.