Anisotropic growth of buckling-driven wrinkles in graphene monolayer

We theoretically and numerically investigate the growth of buckling-driven wrinkles in graphene monolayers. It is found that the growth of buckling-driven wrinkles in a graphene monolayer is remarkably chirality- and size-dependent. In small sizes, the flexural response of a graphene sheet cannot be accurately described by the classical Euler regime, and the non-continuum effect leads to zigzag-along-preferred buckling. With the increase of size, the width/length ratio α of the compressed region plays an important role in the growth of buckling-driven wrinkles. When α < 0.5, the oblique buckling happens in armchair-along compression; when 0.5 < α < 1.0, the effect of edge warp leads to zigzag-along-preferred buckling. When 1.0 < α < 3.0, the potential energy density difference due to chiral bending stiffness leads to armchair-along-preferred buckling. When α > 3.0, the non-continuum effect and chiral bending stiffness can both be neglected, and the buckling in a graphene monolayer is isotropic. The chirality-along-preferred transition of compressed buckling in a graphene monolayer leads to an improved fundamental understanding of the dynamics mechanism of graphene-based nanodevices, especially for the nanodevices with high frequency response.