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

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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 waveequation 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.

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