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...