Confined buckling in thin sheets and its correlation to ripplocations: A deformation mechanism in layered solids
Hussein O. Badr, Xingyuan Zhao, Stylianos Koumlis, Garritt J. Tucker, Leslie Lamberson, Michel W. Barsoum
Abstract
Recently, we have established that, when loaded in compression, edge-on, atomic layers in layered solid can fail by buckling. The resulting structure is termed a ripplocation. When more than one layer buckles, they outline standing waves with boundaries that we labeled ripplocation boundaries that are nearly fully recoverable. In this paper, we examine buckling of layers at the centimeter level to explore continuum buckling theory and its applicability to atomic layers. Specifically, we examine buckling by confining and cyclically loading thin steel sheets, edge-on, determining that increasing confining pressure, sheet thickness, and/or decreasing the number of layers increases the buckling load. Concomitantly, the resulting wavelengths and amplitudes are reduced. A nonlinear, folding mechanics model, which accounts for frictional bending and foundation energies, is adapted and verified on our experimental results. We also demonstrate that Coulombic friction between the layers can account for the energy dissipated per cycle. The predicted values of buckling nucleation loads and number of modes from the model are in good agreement---at low levels of confinement---with continuum and atomistic scale results. The wavelength estimates from the model correlate surprisingly well with the continuum buckling results; however, likely due to the complex mechanics at the lower length scales and limiting theoretical assumptions in the derivation, the accuracy decreases at the atomistic scale and at higher confining pressures.