Effective dynamic properties of random nanoporous materials with consideration of surface effects

The frequency-dependent dynamic effective properties (velocity, attenuation and elastic modulus) of nanoporous materials with randomly positioned spherical cavities are studied. The surface energy theory proposed by Huang and Wang (Handbook of micromechanics and nanomechanics. Pan Stanford Publishing Pte Ltd., Singapore, pp 303-348, 2013) is used to derive the non-traditional boundary condition on the surface of the nanocavity and further the scattering matrix of a single nanocavity. Then, the total wave field is obtained by considering the multiple scattering processes among the dispersive spherical cavities. The configuration average of the total wave field results in the coherent waves or the averaged waves. The numerical examples of the effective speed, the effective attenuation of the coherent waves and associated effective dynamic modulus of a nanoporous material are given and shown graphically. The effects of surface elasticity and the residual surface tension are both considered. Moreover, the influences of the non-symmetric parts of in-plane surface stress and the out-of-plane parts of the surface stress are also discussed based on the numerical examples.