A new mesh-free method to simulate the mechanical behavior of atomic-scale material structures

Numerical methods that are used to analyse materials at the atomic-scale have some limitations. the molecular dynamics (MD) is time-consuming and not suitable for large-scale applications. The atomic-scale finite element method (AFEM) presents some difficulties when defining the element since the atomic element matrices sizes depend on the number of the neighbouring atoms and a special processing is needed for boundary elements. To overcome this issue, a new atomic scale mesh free method (ASMFM) is developed in this study. Moreover, a standard finite element is defined to fit everywhere in the atomic structure. The calculation of the standard element stiffness matrix is based on the atomic bonding potential. The formulation of the ASMFM is implemented to analyze the atomic structures behavior using the Lennard Jones interatomic potential and a mesh free approach. In this approach, the classical meshing is replaced by a function that determines all the possible atomic interactions of a structure. This function depends on the interatomic distances and the cut-off radius of Lennard Jones potential. For a first step, only the covalent bonding structures are tested in this work. The method is applied to different two-dimensional lattices of atomic structures. Compared with classical methods described in the literature, results are encouraging in terms of computational costs of the numerical simulation and accuracy. The methodology can be expanded to be applied for any other atomic domain or material structure described by an interatomic potential energy.