A Numerical Approach To Effective Viscoelastic Properties Of Fiber Composites

Abstract

Composite materials of polymeric base show considerable time dependence in their
mechanical properties. In the present work, the effective viscoelastic behavior of onedirectional
fiber composites, based on components properties and geometry, is determined.
The numerical approach proposed is based upon the theory of periodic homogenization -
Sanchez-Palencia. We use expansions of the periodic component of displacements by means of
Fourier series or alternatively Chebyshev polynomials (modified in order to fulfill periodic
conditions).
The viscoelastic localization problem is solved as a sequence of elastic problems with initial
viscoelastic strains. The solution of each elastic problem is achieved through minimization of
a functional with respect to the coefficients of the displacement expansions (Fourier or
Chebyshev).
Results obtained for the elastic case agree with solutions in the literature. Viscoelastic results
are compared with analytical and numerical (finite element) results.
The advantage of the proposed method is its generality. In particular, it may be used with no
fundamental changes for aging viscoelastic materials.