A multiscale finite element method for the dynamic analysis of surfacedominated nanomaterials

The purpose of this article is to present a multiscale finite element method that captures nanoscale surface stress effects on the dynamic mechanical behavior of nanomaterials. The method is based upon arguments from crystal elasticity, i.e. the Cauchy–Born rule, but significantly extends the capability of the standard Cauchy–Born rule by accounting for critical nanoscale surface stress effects, which are well known to have a significant effect on the mechanics of crystalline nanostructures. We present the governing equations of motion including surface stress effects, and demonstrate that the methodology is general and thus enables simulations of both metallic and semiconducting nanostructures. The numerical examples on elastic wave propagation and dynamic tensile and compressive loading show the ability of the proposed approach to capture surface stress effects on the dynamic behavior of both metallic and semiconducting nanowires, and demonstrate the advantages of the proposed approach in studying the deformation of nanostructures at strain rates and time scales that are inaccessible to classical molecular dynamics simulations. Copyright q 2010 John Wiley & Sons, Ltd.