DETERMINING ELASTIC BEHAVIOR OF COMPOSITES BY THE BOUNDARY-ELEMENT METHOD

The boundary element method is applied to determine the effective elas tic moduli of continuum models of composite materials. In this paper, we specialize to the idealized model of hexagonal arrays of infinitely long, aligned cylinders in a matrix (a model of a fiber-reinforced ma terial) or a thin-plate composite consisting of hexagonal arrays of di sks in a matrix. Thus, one need only consider two-dimensional elastici ty, i.e., either plane-strain or plane-stress elasticity. This paper e xamines a variety of cases in which the inclusions are either stiffer or weaker than the matrix for a wide range of inclusion volume fractio ns phi2. Our comprehensive set of simulation data for the elastic modu li are tabulated. Using the boundary element method, a key microstruct ural parameter eta2 that arises in rigorous three-point bounds on the effective shear modulus is also computed. Our numerical simulations of the elastic moduli for the hexagonal array are compared to rigorous t wo-point and three-point bounds on the respective effective properties . In the extreme instances of either superrigid particles or voids, we compare analytical relations for the elastic moduli near dilute and c lose packing limits to our simulation results.