ANALYTICAL EXPRESSIONS FOR THE RELAXATION MODULI OF LINEAR VISCOELASTIC COMPOSITES WITH PERIODIC MICROSTRUCTURE

In this paper the viscoelastostatic problem of composite materials wit h periodic microstructure is studied. The matrix is assumed linear vis coelastic and the fibers elastic. The correspondence principle in visc oelasticity is applied and the problem in the Laplace domain is solved by using the Fourier series technique and assuming the Laplace transf orm of the homogenization eigenstrain piecewise constant in the space, Formulas for the Laplace transform of the relaxation functions of the composite are obtained in terms of the properties of the matrix and t he fibers and in function of nine triple series which take into accoun t the geometry of the inclusions. The inversion to the time domain of the relaxation and the creep functions of composites reinforced by lon g fibers is carried out analytically when the four-parameter model is used to represent the viscoelastic behavior of the matrix. Finally, co mparisons with experimental results are presented.