Microscopic instabilities and elastic wave propagation in finitely deformed laminates with compressible hyperelastic phases

The compressible laminates require larger strains to trigger mechanical instabilities. This results in lower amplitudes of instability induced wavy patterns in compressible laminates as compared to incompressible layered materials. The instability induced wavy patterns give rise to tunability of the widths and locations of shear wave band gaps (that are not tunable by deformation in LCs with neo-Hookean phases in the stable regime); this tunability, however, is not significant in comparison to the tunability of the pressure wave band gaps. Thus, the complete band gaps (frequency ranges where neither shear nor pressure wave can propagate) can be controlled by deformation in both stable and post-buckling regimes.