Effects of surface and interface energies on the bending behavior of nanoscale multilayered beams

• A modified continuum model of the nanoscale multilayered beams is established by incorporating the surface and interface energies.
• Effects of surface and interface energies on the bending behavior and the overall Young’s modulus of the beam are obtained in closed-form.
• The positive surface elasticity and surface/interface energy will make the beam stiffer.
• The negative surface elasticity and surface/interface energy will make the beam softer.
• The surface/interface effect of nanoscale multilayered materials can be determined by bending experiments.

A modified continuum model of the nanoscale multilayered beams is established by incorporating surface and interface energies. Through the principle of minimum potential energy, the governing equations and boundary conditions are obtained. The closed-form solutions are presented and the overall Young's modulus of the beam is studied. The surface and interface energies are found to have a major influence on the bending behavior and the overall Young's modulus of the beam. The effect of surface and interface energies on the overall Young's modulus depends on the boundary condition of the beam, the values of the surface/interface elasticity constants and the initial surface/interface energy of the system. The results can be used to guide the determinations of the surface/interface elasticity properties and the initial surface/interface energies of the nanoscale multilayered materials through nanoscale beam bending experiments.