An Optimized Mesh-Free Method Using an Auto-determination of Atomic Interactions to Simulate the Mechanical Behavior of Covalent Bonding Structures

The Molecular Dynamics (MD) and the Atomic-scale Finite Element Method (AFEM) are largely used to analyse the atomic scale structures behaviour, but they present some disadvantages. The MD has high computational costs and is suitable only for small applications while the AFEM presents some difficulties of formulation and implementation because each atomic element matrix size depends on the neighbouring atoms and the boundary elements need a special processing. To overcome these difficulties, a standard finite element is formulated and used in the development of an Atomic-Scale Mesh-Free Method (ASMFM). This new optimized method is used to analyze the mechanical response of atomic structures to an external loading. To replace the classical meshing, all the atomic interactions of the structure are determined using a function that depends on the interatomic distances and the cut-off radius of Lennard Jones potential. For comparison raisons, only the covalent bonding structures are considered in the simulation. The method is applied to one- and two-dimensional atomic structures. Results show a low computational cost and an acceptable accuracy when compared with those of classical methods. The ASMFM methodology has encouraging results and can be applied for others materials and atomic structures described by an interatomic potential energy.