Elastic waves in fluid-saturated porous materials with a couple-stress solid phase

Abstract

Fluid-saturated porous materials have attracted extensive attention in micro/nanoscale applications owing to their excellent mechanical properties. Couple-stress theory can be used to depict the size effect of micro/nanoelastic materials, which cannot be ignored when the internal characteristic length of materials is comparable with the material size or wavelength. However, it has not been extended to porous materials. In this paper, we investigate the size effect of elastic-wave propagation in micro/nano fluid-saturated porous materials by combining couple-stress theory with Biot theory and introducing the higher order micro-inertia effect, establish the motion equations for elastic waves in fluid-saturated porous materials containing a couple-stress solid phase. The reflection and transmission properties of elastic waves at the interface between an elastic solid and a couple-stress fluid-saturated porous material are numerically analyzed. The results suggest that an increase in characteristic length can lead to an increase in the phase velocity of shear wave and further influence the reflection and transmission of elastic waves. A comparison among the proposed theory, Biot theory and experimental data indicates that the introduction of couple-stress and higher order micro-inertia effects allows for a more accurate calculation of the propagation properties of elastic waves in fluid-saturated porous materials, and it can provide a theoretical basis for applications of elastic waves in micro/nano porous materials, such as nondestructive testing.