Wave propagation of Rayleigh waves in bones: A gradient viscoelastic approach

Bone is a inhomogeneous hierarchical material with different microstructure at different length scales. On the other hand, the constituent materials (mineral, proteins, water and polysaccharides) and the fluid in bone pores give rise of viscoelastic behavior. In the present work, the effect of bones mi-crostructure and its viscoelastic properties on the propagation of Rayleigh waves is investigated. Microstructural effects are taken into account through Mindlin´s general gradient elastic theory. A composite material model proposed by Ben-Amoz is employed for the determination of the intrinsic parameters imposed by Mindlin´s theory. Viscoelasticity is introduced via convolution integrals and proper relaxation functions valid for bones. All the gradient viscoelastic problems are solved via the Boundary Element Method and exploiting the correspondence principle. The results reveal that both microstructure and viscoelastic properties affect significantly the propagation and dispersion of Rayleigh waves in long bones.