International Journal for Multiscale Computational Engineering

ISSN for PRINT: 1543-1649

For Online Access

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2006, Volume4

Issue 5-6

271 pages

DOI: 10.1615/IntJMultCompEng.v4.i5-6

Issue price - $256.00

Robert P. Gilbert
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, U.S.A.

Alexander Panchenko
Department of Mathematics, Washington State University, Pullman, WA 99164, USA

Xuming Xie
Department of Mathematics, Morgan State University, Baltimore, MD, USA

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.

DOI: 10.1615/IntJMultCompEng.v4.i5-6.30 Download article, 585-600 pages

Article price - $35.00

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