Analysis of surface effects using the theory of second-order strain gradient elasticity

Abstract

In this study, we investigate the effect of surface energy on the nano-scale object using the theory of second strain gradient elasticity. This theory adds the first- and second-order gradients of strain to constitutive equations of the classical elasticity. The characteristic length scales, which represents the size of the microscopic structure of the material, and the surface energy are introduced into the constitutive equations. We solve the variational problem by using the isogeometric analysis; Galerkin method with non-uniform B-spline basis function. Strain energy density is simplified by using the irreducible decomposition of elasticity tensors under the general linear group GL(3). We conducted a numerical analysis for a hollow torus-shaped isotropic elastic medium. We observed that the surface displacement tends to dominate as the size of the material approaches the nanoscale.