The effect of nonlinear elastic pre-stress on antiplane elastic wave propagation in a two-
dimensional periodic structure is investigated. The medium consists of cylindrical annuli
embedded on a periodic square lattice in a uniform host material. An identical
inhomogeneous deformation is imposed in each annulus and the theory of small-on-large is
used to find the incremental wave equation governing subsequent small-amplitude
antiplane waves. The plane-wave-expansion method is employed in order to determine the …