A Model for Large Deflections of Nanobeams and Experimental Comparison

Bending tests are commonly used for characterization of materials at the nanoscale. Beams are also key elements of nanomechanical and nanoelectromechanical devices. This paper is motivated by recent experiments of large deflections of chromium cantilevers and modeling based on the classical large deflection beam theory to simulate experiments. A review of nanobeam experiments shows complex size dependency of elastic modulus that is influenced by beam thickness (or diameter) and end boundary conditions. A new large deflection beam model that accounts for surface energy effects is presented. It is shown that the model is capable of simulating experiments by using size-independent properties such as bulk elastic modulus and surface residual stress. The model is then used to explain the softening or stiffening behavior observed experimentally in nanocantilevers and relative size independence of clamped-clamped beams. Size dependence of elastic modulus (or stiffening/softening) is a modeling artifact introduced due to the use of classical elasticity theory for nanostructures and the current model shows that simulations based on classical beam theory require careful interpretation.