Finite element model of ionic nanowires with size-dependent mechanical properties determined by ab initio calculations

A finite element procedure for modeling crystalline nanostructures such as nanowires is proposed. The size effects exhibited by nano objects are captured by taking into account a surface energy, following the classical Gurtin Murdoch surface elasticity theory. An appropriate variational form and a finite element approach are provided to model and solve relevant problems numerically. We describe a simplified technique based on projection operators for constructing the surface elements. The methodology is completed with a computational procedure based on ab initio calculations to extract elastic coefficients of general anisotropic surfaces. The FEM continuum model is validated by comparisons with complete ab initio models of nanowires with different diameters where size-dependent mechanical properties are observed. The FEM continuum model can then be used to model similar nanostructures in ranges of sizes or geometries where analytical or atomistic model are limited. The validated model is applied to the analysis of size effects in the bending of an AlN nanowire.