Plane waves in a hypoplastic half-space under periodic boundary conditions

The paper presents a numerical study of the propagation of plane waves in a half-space occupied by a granular material, with periodic boundary conditions for velocity or stresses prescribed at the boundary of the half-space. The constitutive behaviour of the material is described by a simplified hypoplastic equation which takes into account different values of the stiffness for different directions of deformation, and the coupling between shear and volumetric strains owing to dilatancy. These two features are responsible for a nonlinear character of longitudinal waves and for the generation of longitudinal motion by transverse disturbances. It is shown that longitudinal and transverse boundary disturbances produce qualitatively the same longitudinal waves at large distances from the boundary. As a longitudinal wave propagates, the amplitude of oscillations decreases and eventually vanishes, resulting in a single non-oscillating wave.