  Hexagonal layered crystalline materials, such as graphene, boron nitride,
tungsten sulfate, and so on, have attracted enormous attentions, due to their
unique combination of atomistic structures and superior thermal, mechanical,
and physical properties. Making use of mechanical buckling is a promising route
to control their structural morphology and thus tune their physical properties,
giving rise to many novel applications. In this paper, we employ finite element
analysis (FEA), molecular dynamic (MD) simulations and continuum modeling to
study the mechanical buckling of a column made of layered crystalline materials
with the crystal layers parallel to the longitudinal axis. It is found that the
mechanical buckling exhibits a gradual transition from a bending mode to a
shear mode of instability with the reduction of slenderness ratio. As the
slenderness ratio approaches to zero, the critical buckling strain {\epsilon}cr
converges to a finite value that is much smaller than the material's mechanical
strength, indicating that it is realizable under appropriate experimental
conditions. Such a mechanical buckling mode is anomalous and counter-intuitive.
The critical buckling strain {\epsilon}cr predicted by our continuum mechanics
model agrees very well with the results from the FEA and MD simulations for a
group of typical hexagonal layered crystalline materials. MD simulations on
graphite indicate the continuum mechanics model is applicable down to a scale
of 20 nm. This theoretical model also reveals that a high degree of elastic
anisotropy is the origin for the anomalous mechanical buckling of a column made
of layered crystalline materials in the absence of structural slenderness. This
study provides avenues for engineering layered crystalline materials in various
nano-materials and nano-devices via mechanical buckling.
