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

In this paper, we study the elastic instability and wave propagation in compressible layered composites undergoing large deformations. We specifically focus on the role of compressibility on the onset of instability, and elastic wave band gaps (forbidden frequency ranges) in finitely deformed buckled laminates. We employ the Bloch-Floquet analysis to study the influence of compressibility on the onset of instability and the corresponding critical wavelengths. Then, the obtained information about the critical wavelengths is used in the subsequent numerical postbuckling simulations. By application of the Bloch wave numerical analysis implemented in the finite element code, we investigate the elastic wave band gaps of buckled layered composites with compressible 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.