A molecular dynamics derived Finite Element Method for structural simulations and failure of graphene nanocomposites

Abstract

The recent rise of 2D materials, such as graphene, has expanded the interest in nanoelectromechanical systems (NEMS). The increasing ability of synthesizing more exotic NEMS architectures, creates a growing need for a cost-effective, yet accurate nano-scale simulation method. Established methodologies like Molecular Dynamics (MD) trail behind synthesis capabilities because the computational effort scales quadratically. The equilibrium equations of MD are equivalent with those of the computationally more favourable Finite Element Method (FEM). However, current implementations exploiting this equivalence remain limited due to the FEM iterative solvers requiring a large number of lengthy force field derivatives and specifically tailored element topologies. This paper proposes a merged Molecular Dynamic Finite Element Method (MDFEM) which does not require the manual derivation of these derivatives. Hence, implementing MDFEM-specific element topologies is straightforwards and thus, different non-linear MD force field potentials can be solved exactly within the FEM, at reduced computational costs. The proposed multi-scale and multi-physics compatible MDFEM is equivalent to the MD, as demonstrated firstly by an example of brittle fracture in Carbon Nanotubes (CNT), and secondly by conformational analyses on Non-Equilibrium initial meshes of Pillared Graphene Structures (PGS).