ALGORITHM FOR COMPUTING THE EFFECTIVE LINEAR ELASTIC PROPERTIES OF HETEROGENEOUS MATERIALS - 3-DIMENSIONAL RESULTS FOR COMPOSITES WITH EQUAL PHASE POISSON RATIOS

An algorithm based on finite elements applied to digital images is des cribed for computing the linear elastic properties of heterogeneous ma terials. As an example of the algorithm, and for their own intrinsic i nterest, the effective Poisson's ratios of two-phase random isotropic composites are investigated numerically and via effective medium theor y, in two and three dimensions. For the specific case where both phase s have the same Poisson's ratio (nu(1) = nu(2)), it is found that ther e exists a critical Value nu, such that when nu(1) = nu(2) > v*, the composite Poisson's ratio nu always decreases and is bounded below by nu when the two phases are mixed. If nu(1) = nu(2) < nu*, the value o f nu always increases and is bounded above by nu when the two phases are mixed. In ii dimensions, the value of nu is predicted to be 1/(2d - 1) using effective medium theory and scaling arguments. Numerical re sults are presented in two and three dimensions that support this pict ure, which is believed to be largely independent of microstructural de tails.