BEM simulations of Rayleigh wave propagation in media with microstructural effects: Application to long bones

Bone is a strongly heterogeneous natural composite with microstructure. Although the classical theory of linear elasticity has been largely used in bone ultrasonic studies, it cannot sufficiently describe the mechanical behavior of materials with microstructure. Furthermore, this theory predicts non-dispersive behavior of Rayleigh waves, which is in conflict with experimental observations. By using the simplest theory of gradient elasticity we recently demonstrated that bone´s microstructure significantly affects the dispersion of classical Lamb modes. In this work, we investigate the effect of bone´s microstructure on the propagation of Rayleigh waves by using the Boundary Element Method (BEM). We assume an isotropic semi-infinite space with mechanical properties equal to those of bone and microstructure. Microstructural effects are taken into account by introducing in the stress analysis the internal length scale parameters l₁, l₂, h₁, h₂. BEM computations are performed for various combinations of these parameters with values empirically chosen close to the osteon´s size. The constants´ values are also compared to those derived from closed form relations. The results made clear that bone´s microstructure significantly affects Rayleigh wave dispersion.