ABSTRACT
The Boundary Element Method (BEM) is a very well known and robust numerical tool successfully used for the solution of wave scattering problems. Two remarkable advantages it offers as compared to other numerical methods is the reduction of the dimensionality of the problem by one and its high solution accuracy. Despite the advantages the brutal application of BEM to large-scale problems, like that of scattering by a large number of fibers, suffers from very time consuming computations and high demands for computer memory capacity. Both problems come from the generation of the non-symmetric coefficient matrix [A] and the solution of the final system of algebraic equation [A] ⋅ {x} = {b}. More precisely, the fully populated matrices produced by BEM require O(N2)
1 INTRODUCTION
The propagation of a plane wave in particulate and fiber composites is always characterized by dispersion and attenuation due to its multiple scattering by the embedded in-homogeneities. Thus, even in the case where the constituents of the composite are non-dispersive and non-attenuative materials, any elastic wave propagating in the main body of the composite undergoes both dispersion and attenuation. A methodology of estimating the dispersive and attenuative properties of a composite elastic medium is that of Iterative Effective Medium Approximation (IEMA) proposed by Tsinopoulos et al. (2000), Verbis et al. (2001) and Aggelis et al. (2004). The IEMA makes use of the single inclusion self-consistent condition of Kim et al. (1995) and assumes that the effective stiffness of the composite is the same with the corresponding static one and evaluates iteratively the effective and frequency dependent dynamic density of the composite. The complex value of the effective dynamic density and the static effective stiffness of the composite determine, eventually, the wave speed and the attenuation coefficient of the plane wave propagating through the composite material.
