Characterization of Stiffness Matrix for Surface Effects

The stiffness matrix of volume elements in the traditional finite element methods is symmetry and positive definite. Due to the relatively high surface-to-volume ratio, the surface effect can be significant for nanostructures. In a new numerical method which combines surface energy and three-dimensional finite element analysis, the stiffness matrix with surface effects was computed numerically. Results show the stiffness matrix of surface elements is symmetry and non-positive definite.