How surface tension influences effective velocities and dispersion of elastic waves in unidirectional porous materials

Abstract

Surface stress is known to affect significantly the mechanical behavior of micro- or nano-porous materials. Total surface stress is usually divided into the (initial) surface tension and the surface stretching strain-dependent surface stress related to surface elasticity. The effects of surface elasticity on the effective dynamic properties of porous materials have been well studied in the literature via the use of a simplified version of the Gurtin-Murdoch model which, however, fails to capture corresponding surface tension effects (due to the exclusion of an important surface displacement gradient or equivalently that of the deformation-induced change in the normal direction and curvature of the material surface from this simplified version). In this paper, we employ the complete version of the Gurtin-Murdoch model and the generalized self-consistent method to explore the effects of surface tension on the overall transverse dynamic behavior of a unidirectional porous material. Numerical examples are presented for a soft elastic medium with cylindrical pores at submicron scales. We find that compared with surface elasticity, surface tension plays only a minor role in determining the effective velocity of compressional waves in the microporous medium while it has a comparably significant positive influence on the effective velocity of shear waves (despite the fact that the value of surface tension is much smaller than that of the surface stretching modulus). In particular, we demonstrate that the presence of surface tension reduces significantly the sensitivity of the effective shear-wave velocity to the wave frequency, leading to almost non-dispersive shear wave propagation in the microporous medium in a wide wave-frequency range.