# Bending rigidity of the nanomaterial from MD simulation

The literature seems to be very diverse in measuring the bending rigidity of the nanomaterial from MD simulation. I have seen people often use this relation from continuum mechanics $$k = \frac{Eh^3}{12(1-\nu^2)}$$ for measuring the bending rigidity, but with the cubic dependence of this relation on the thickness of the material, and not a precise way of finding poisson's ratio ($$\nu$$), it seems to be difficult. Has anyone tried this method, or any others, to compute the bending rigidity, which gives results similar to the experiments? Thanks.

With best regards

You are absolutely right to be skeptical about applying continuum equations carelessly to nanostructures. If a nanostructure is soft / small enough that significant deformations only require energies on the order of a few $$k_BT$$, then the canonical ensemble of the nanostructure will include significant contributions from deformed states, and you need polymer theoretical physics to inform you about the free energy of deformation.