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An Asymptotic Method for Effective Properties of Visco‐Elastic Composite Materials
Author(s) -
Aadrianov I. V.,
Danishevs'kyy V. V.,
Toearzewski S.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.20000801457
Subject(s) - asymptotic homogenization , composite number , viscoelasticity , materials science , homogenization (climate) , shear modulus , laplace transform , mathematical analysis , tangent , composite material , mathematics , geometry , biodiversity , ecology , biology
We consider visco‐elastic two‐components composite materials, consisting of an infinite regular arrays of fibers inclusions embedded in a matrix. Analytical formulas for Laplace transforms of the effective shear relaxation and creep functions are derived. For this aim an asymptotic technique, based on the homogenization method, the three‐phase model, the method of boundary perturbation, Pade and quasifractional approximants, is used Obtained results also allow us to evaluate the effective complex shear modulus and loss tangent for stationary harmonic oscillations of considered composite material. Derived solutions are valid for all values of the components concentrations and properties. Our method may be effectively used for determining various effective properties of visco‐elastic composite materials with different inclusions geometries.