ACCURACY OF THE GENERALIZED SELF-CONSISTENT METHOD IN MODELING THE ELASTIC BEHAVIOR OF PERIODIC COMPOSITES

Local stress and strain fields in the unit cell of an infinite, two-di mensional, periodic fibrous lattice have been determined by an integra l equation approach. The effect of the fibres is assimilated to an inf inite two-dimensional array of fictitious body forces in the matrix co nstituent phase of the unit cell. By subtracting a volume averaged str ain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the ove rall stress and strain correspond to the volume averaged stress and st rain of the constrained unit cell. This paper demonstrates that the ze roth term in the governing integral equation expansion, which embeds o ne unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation By comparing the zeroth term approximat ion with higher order approximations to the integral equation summatio n, both the accuracy of the generalized self-consistent composite mode l and the rate of convergence of the integral summation can be assesse d. Two example composites are studied. For a tungsten/copper elastic f ibrous composite the generalized self-consistent model is shown to pro vide accurate, effective, elastic moduli and local field representatio ns. The local elastic transverse stress field within the representativ e volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.