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Mathematics and Mechanics of Solids
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The Effect of Imperfect Contact on the Homogenization of a Micro-periodic Helix

J.M. Vivar-Perez

Facultad de Matemática y Computación, Universidad de La Habana, San Lazaro y L, Vedado, CP 10400, La Habana, Cuba

J. Bravo-Castillero

Facultad de Matemática y Computación, Universidad de La Habana, San Lazaro y L, Vedado, CP 10400, La Habana, Cuba

R. Rodriguez-Ramos

Facultad de Matemática y Computación, Universidad de La Habana, San Lazaro y L, Vedado, CP 10400, La Habana, Cuba

M. Ostoja-Starzewski

Department of Mechanical Science & Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

Under study are the equations governing the elastodynamics of a micro-periodic helix, i.e. a helix made of a sequence of unit cells, each containing a thin imperfect interphase embedded within a finite number of other phases. An averaged equation of motion, along with its effective constitutive coefficients, is determined via an asymptotic homogenization method. The results are valid in the case of wavelengths much longer than the length of the unit cell. Formulae for shorter wavelengths can be derived by admitting higher order terms in the expansion.

Key Words: helix • elastodynamics • homogenization • imperfect interface • periodic structure

This version was published on July 1, 2008

Mathematics and Mechanics of Solids, Vol. 13, No. 5, 431-446 (2008)
DOI: 10.1177/1081286507077336
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