  Two-dimensional materials were first isolated no longer than ten years ago,
and a comprehensive understanding of their properties under non-planar shapes
is still being developed. Strictly speaking, the theoretical study of the
properties of graphene and other two-dimensional materials is the most complete
for planar structures and for structures with small deformations from
planarity. The opposite limit of large deformations is yet to be studied
comprehensively but that limit is extremely relevant because it determines
material properties near the point of failure. We are exploring uses for
discrete differential geometry within the context of graphene and other
two-dimensional materials, and these concepts appear promising in linking
materials properties to shape regardless of how large a given material
deformation is. A brief account of additional contributions arising from our
group to two-dimensional materials that include graphene, stanene and
phosphorene is provided towards the end of this manuscript.
