First-principle approach to the calculation of elastic moduli for arbitrary periodic composites

Abstract

We present a first-principle approach to the calculation of effective elastic moduli for arbitrary periodic composites. The method is based on the iterative solution of the inhomogeneous elastic wave equation in wave-vector space. By using Fourier coefficients of the periodic system as structural inputs, the present approach offers the advantage of circumventing the need for explicit boundary-conditions matching across interfaces. As a result, it can handle complex unit-cell geometries just as easily as simple cell geometries. We illustrate the application of this method by calculating the effective moduli of (1) a three-dimensional porous frame composed of a simple cubic array of fused solid spheres, and (2) a periodic two-component composite.