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The recent rise of 2D materials, such as graphene, has expanded the interest in nano-electromechanical 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 re- main 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 formal deriva- tion of the merged Molecular Dynamic Finite Element Method (MDFEM) which establishes an uncoupling of the force field potentials from the element topologies. An implementation approach, which does not require manual derivations, is presented. Different non-linear MD forcefield potentials are implemented exactly within the FEM, at reduced computational costs. The proposed multi-scale and multi-physics compatible MDFEM is equivalent to to the MD as demonstrated by an example of brittle fracture in Carbon Nanotubes (CNT).

A Molecular Dynamics derived Finite Element Method for Structural Simulations and Failure of Graphene Nanocomposites