Thermalized Euler buckling in clamped ribbons with variable aspect ratio.

Micro structures such as cantilevers made by cutting graphene sheets have recently been studied experimentally in great detail with application in NEMS and MEMS [1]. To better design such mechanical resonators one needs to understand the dependence of thermal buckling on the aspect ratio of the mechanical resonator. It is well known that thermal fluctuations renormalize the bending rigidity of elastic membranes, leading to power-law stiffening as a function of system size. We explore ribbons clamped at both ends via Molecular Dynamics simulations [2]. We find that by changing the aspect ratio at a fixed temperature one can tune the onset of buckling in these ribbons. Ribbons with large aspect ratio feel stronger effects of clamping and are flat compared to low aspect ratio ribbons. We also study the compressive forces required to buckle ribbons of higher aspect ratio.

[1] C. Chen et.al, Nature Communications 15523 (2017)
[2] S.Bhabesh, D.Yllanes, Mark Bowick. Manuscript in progress