  Morphology mediates the interplay between the structure and electronic
transport in atomically thin nanoribbons such as graphene as the relaxation of
edge stresses occurs preferentially via out-of-plane deflections. In the case
of end-supported suspended nanoribbons that we study here, past experiments and
computations have identified a range of equilibrium morphologies, in particular
for graphene flakes, yet a unified understanding of their relative stability
remains elusive. Here, we employ atomic-scale simulations and a composite
framework based on isotropic elastic plate theory to chart out the
morphological stability space of suspended nanoribbons with respect to
intrinsic (ribbon elasticity) and engineered (ribbon geometry) parameters, and
the combination of edge and body actuation. The computations highlight a rich
morphological shape space that can be naturally classified into two competing
shapes, bending-like and twist-like, depending on the distribution of ripples
across the interacting edges. The linearized elastic framework yields exact
solutions for these rippled shapes. For compressive edge stresses, the body
strain emerges as a key variable that controls their relative stability and in
extreme cases stabilizes co-existing transverse ripples. Tensile edge stresses
lead to dimples within the ribbon core that decay into the edges, a feature of
obvious significance for stretchable nanoelectronics. The interplay between
geometry and mechanics that we report should serve as a key input for
quantifying the transport along these ribbons.
