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Homogenization of a viscoelastic matrix in linear frictional contact
Author(s) -
Gilbert Robert P.,
Panchenko Alexander,
Xie Xuming
Publication year - 2005
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.570
Subject(s) - homogenization (climate) , viscoelasticity , dissipation , drag , matrix (chemical analysis) , mechanics , classical mechanics , contact force , materials science , mathematics , mathematical analysis , physics , composite material , thermodynamics , biodiversity , ecology , biology
The paper is devoted to study of acoustic wave propagation in a partially consolidated composite material containing loose particles. Friction of particles against the consolidated part of the material causes mechanical energy dissipation. This situation is modelled by assuming that the medium has a periodic microstructure changing rapidly on the small scale ε. Each of the periodic microscopic cells is composed of a viscoelastic matrix containing a rigid particle in frictional contact with the matrix. We use the methods of two‐scale convergence to obtain effective acoustic equations for the homogenized material. The effective equations are history‐dependent and contain the body force term, reminiscent of the well‐known Stokes drag force. Copyright © 2004 John Wiley & Sons, Ltd.