Elastic instabilities and shear waves in hyperelastic composites with various periodic fiber arrangements

We investigate the influence of fiber arrangement on elastic instabilities and shear wave propagation in hyperelastic 3D fiber composites (FCs) with periodic rectangular arrays of cylindrical fibers. We show that elastic instabilities and shear waves propagating along the fibers in uniaxially deformed FCs can be tuned through the choice of the periodicity of fiber arrangements (or periodic unit cell aspect ratio b/a) of FCs. In particular, we find that the range of deformations, where FCs are mechanically stable, decreases with an increase in the periodicity aspect ratio. Moreover, we identify the bounds for the critical stretches in FCs with periodic rectangular arrays of fibers. We find that the FC critical stretches are bounded by the critical values for corresponding 3D laminates (upper bound) and FCs with square arrays of fibers (lower bound). In FCs with large volume fractions of fibers (e.g. 25%), the polarization directions of the long shear waves start rotating upon approaching critical deformation. This indicates that fibers develop buckling shapes in non-principal planes. In FCs with small volume fractions of fibers (e.g. 5%), polarizations of the shear waves (of the lowest frequencies) barely changes the direction upon attaining the critical deformation; hence, buckling of fibers initially develops in one of the principal planes, depending on the periodicity aspect ratio of FCs.