Sharif Digital Repository

Mindboggling advances in nanotechnology have urged researchers to develop state-of-the-art numerical methods to enable them to simulate and to interpret phenomena at this scale. Unfortunately, Classical models have numerous shortcomings which hinder their applications in new contexts. For instance, classical Continuum Mechanics fails to appropriately depict material behavior at small scales, and, on the other hand, Molecular Dynamics simulations are computationally prohibitive. As a consequence, researchers have devised multi-scale methods during the past decade to overcome these obstacles. In fact, in multi-scale methods information is passed from one mathematical description to the other.... 

Nanocrystalline materials have received increasing attention during the last decades. Polycrystalline structures with grain sizes less than 100 nm are referred as nanocrystalline (NC). Their mechanical properties differ significantly from polycrystalline structures. As an example, hardness and wear resistance of nanocrystalline structures are higher than those of polycrystalline structures. With the reduction of grain size, hardness increases based on the Hall–Petch relation. However, at the very small grain sizes the Hall–Petch relation breaks down and a fundamental shift takes place in hardening mechanism. Molecular dynamics (MD) simulation offers a powerful method for the investigation of... 

Crack propagation problem is one of the most important problems that are being investigated for a long time. Plenty of various approaches have been utilized to simulate the crack propagation phenomenon. Continuum based methods like Finite element (FE), Extended Finite element (XFEM), have been successfully applied, and the obtained results are valid in macro scale. However, the stress filed near crack tip in FEM modeling of crack, is not exquisite enough due to inability of continuum based approaches in revealing atomistic aspects of the material.
In order to gather efficiency of the continuum based domain and the accuracy of the atomistic based domain, Multiscale methods are employed.... 

In line with the high computational cost of Molecular Dynamics resulting in restrictions in time and domain, and incompetency of Finite Element method to deal with problems like those consisting of inhomogeneities, where no distinctive constitutive law may be considered, the multi scale methods have extensively settled as an alternative in recent decades. In continuation of preceding studies in the presented research, a concurrent multi scale procedure is employed for coupling MD-FE methods applying Lagrange multiplier approach in order for energy to resemble in transient zone and calculating the stiffness matrix of FE mesh employing the atomic grid laid beneath in order to investigate the...