Dynamic Equivalence of Composite Material and Eigenstrain Problems

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Abstract
The variational method is employed for determining the displacement mode shapes and dispersion relations for the problem of plane time-harmonic waves propagating through an infinitely extended, periodically arranged composite material. Numerical results are obtained for the special cases of laminated and fiber-reinforced media. Using variational formulation, the composite problem is compared with the problem of a homogeneous material subjected to eigenstrain and body forces. Necessary conditions are developed for the dynamic equivalency of the two problems. Distributions of eigenstrain are shown which yield the same displacement solutions as the problem of a transverse wave propagating normal to the layers of a laminated media.

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