Abstract
Effective stiffness properties (D) of nanosized structuralelements such as plates and beams differ from those predicted bystandard continuum mechanics (Dc). These differences(D-Dc)/Dc depend on the size of the structural element. Asimple model is constructed to predict this size dependence ofthe effective properties. The important length scale in theproblem is identified to be the ratio of the surface elasticmodulus to the elastic modulus of the bulk. In general, thenon-dimensional difference in the elastic properties fromcontinuum predictions (D-Dc)/Dc is found to scale as αS/Eh, where α is a constant which depends on thegeometry of the structural element considered, S is a surfaceelastic constant, E is a bulk elastic modulus and h a lengthdefining the size of the structural element. Thus, the quantityS/E is identified as a material length scale for elasticity ofnanosized structures. The model is compared with directatomistic simulations of nanoscale structures using theembedded atom method for FCC Al and the Stillinger-Weber modelof Si. Excellent agreement between the simulations and themodel is found.
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