Interface Effects and Coherent Waves in Porous Elastic Media

Abstract

Results concerning the behavior of interfaces in the presence of multiple scattering are obtained here for the first time. To characterize interface effects, we consider an elastic slab of finite thickness containing a random distribution of circular cylindrical cavities. Using elasticity theory, and taking first-order multiple scattering effects between cavities into account, we obtain two new results. First, inside the slab, within one cavity-diameter from the two slab boundaries, the coherent displacement is strongly inhomogeneous (with singular first and second derivatives). Second, inside the slab, away from the preceding singular regions, the coherent displacement is governed by a complex-valued wavenumber (which is independent of slab thickness). Exhaustive analytical work, together with time-consuming finely-tuned numerical work, has been performed, which has allowed us to evaluate the complex-valued wavenumber. We plot the corresponding speed and attenuation as functions of frequency for various cavity densities. This work will help researchers improve the precision of ultrasound technologies in materials engineering or biomaterials engineering.