RT Journal Article ID 2870b1ba0496294c A1 Gilbert, Robert P A1 Panchenko, Alexander A1 Xie, Xuming T1 A Prototype Homogenization Model for Acoustics of Granular Materials JF International Journal for Multiscale Computational Engineering JO JMC YR 2006 FD 2007-02-08 VO 4 IS 5-6 SP 585 OP 600 AB This paper introduces a homogenization approach to modeling acoustic vibrations of composite materials with internal friction. The model medium studied in the paper consists of a consolidated viscoelastic solid matrix with a large number of periodically arranged pores containing rigid solid particles. The particles are in frictional contact with the matrix. At the length scale of particles, the frictional forces are modeled initially by the Coulomb's law with normal compliance. These inequality-type conditions are approximated by nonlinear equations. The resulting microscale problem is averaged using formal two-scale homogenization. The effective acoustic equations are, in general, nonlinear and history dependent, and contain both effective stress and the effective drag force. The constitutive equations for the effective quantities are obtained explicitly for three different approximate models of contact conditions. PB Begell House LK https://www.dl.begellhouse.com/journals/61fd1b191cf7e96f,1b4adbb73e2792e0,2870b1ba0496294c.html