Bending Stiffness of Circular Multilayer van der Waals Material Sheets

We study the bending stiffness of symmetrically bent circular multilayer van der Waals (vdW) material sheets, which correspond to the nonisometric configuration in bulge tests. Frenkel sinusoidal function is employed to describe the periodic interlayer tractions due to the lattice structure nature and the bending stiffness of sheets is theoretically extracted via an energetic consideration. Our quantitative prediction shows good agreement with recent experimental results, where the bending stiffness of different types of sheets with the comparable thickness could follow a trend opposite to their Young’s moduli. On the basis of our model, we propose that this trend may experience a transition as the thickness decreases. Apart from the apparent effects of Young’s modulus and interlayer shear strength, the interlayer distance is also found to have an important impact on the bending stiffness. In addition, according to our analysis on the size effect, the bending stiffness of such symmetrically bent circular sheets can steadily own a relatively large value, in contrast to the cases of isometric deformations.