Sharif Digital Repository

In this paper the surface effects in 3D complex parts are investigated via classical FEM and the modified boundary Cauchy-Born method, which are continuum based theories, and the results are compared with molecular dynamics simulations. The boundary Cauchy-Born covers the weakness of the surface Cauchy-Born in modeling edge and corner elements, so the results are in better agreement with molecular dynamics simulations. Using super convergent patch recovery method, MBCB shows more precise results in comparison with BCB as it can model acute and obtuse angles which cannot be modeled via BCB. The flexibility of MBCB in modeling 3D complex and non-right angle geometries are utilized to model... 

In this paper, a new multi-scale approach is presented based on the modified boundary Cauchy-Born (MBCB) technique to model the surface effects of nano-structures. The salient point of the MBCB model is the definition of radial quadrature used in the surface elements which is an indicator of material behavior. The characteristics of quadrature are derived by interpolating data from atoms laid in a circular support around the quadrature, in a least-square scene. The total-Lagrangian formulation is derived for the equivalent continua by employing the Cauchy-Born hypothesis for calculating the strain energy density function of the continua. The numerical results of the proposed method are... 

In this paper, a novel multi-scale approach is developed for modeling of the surface effect in crystalline nano-structures. The technique is based on the Cauchy-Born hypothesis in which the strain energy density of the equivalent continua is calculated by means of inter-atomic potentials. The notion of introducing the surface effect in the finite element method is based on the intrinsic function of quadratures, called as an indicator of material behavior. The information of quadratures is derived by interpolating the data from probable representative atoms in their proximity. The technique is implemented by the definition of reference boundary CB elements, which enable to capture not only...