Mechanics of planar periodic microstructures

Abstract

The deformation of two-dimensional periodically patterned elastomeric sheets has been shown to trigger interesting pattern changes that are both repeatable and predictable (Bertoldi et al., 2007). Here, both square and hexagonal lattices of these sheets under axial compression are investigated both with empty voids, and also with inclusions introduced into the voids in specified patterns. A local buckling instability in the square lattice and shear instability in the hexagonal lattice trigger the change in pattern in the structure upon reaching a critical stress during compression. Experimental and numerical results are obtained that show the ability to predict and control the pattern changes that are triggered. The shape of the pattern change, the areas of the lattice in which it is triggered, and the extent to which the pattern is accentuated can all be controlled in a predictable manner. While the results here are on the millimeter length scale, they should also be applicable at the micro- and nano-scales, leading to photonic and phononic applications.