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International Journal for Multiscale Computational Engineering
Facteur d'impact: 1.016 Facteur d'impact sur 5 ans: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352

International Journal for Multiscale Computational Engineering

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

A Prototype Homogenization Model for Acoustics of Granular Materials

Robert P Gilbert
Alexander Panchenko
Department of Mathematics, Washington State University, Pullman, WA 99164, USA
Xuming Xie
Department of Mathematics, Morgan State University, Baltimore, MD, USA

RÉSUMÉ

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.


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