Micromechanical method for determining the effective surface elastic modulus of solids with surface microstructures

The roughness or microstructures of natural and artificial materials significantly affect their surface properties. The performance of micro-sized materials and devices often exhibit a strong dependence on their surface elasticity, but it remains unclear how the surface elastic parameters can be theoretically predicted for rough solid surfaces. In this study, we establish a micromechanical method to determine the macroscopically effective surface elastic moduli of an elastic solid covered with surface microstructures. Both two- and three-dimensional explicit expressions are given to predict the effective surface elastic moduli in terms of the material and geometric parameters of surface microstructures and the bulk body. These solutions work well for a wide variety of geometric shapes of surface microstructures. This work can be used to analyze the mechanical properties of devices and structures with miniatured sizes and to help design advanced functional materials with, for example, quantum dots.