Development of a multi-physics molecular dynamics finite element method for the virtual engineering design of nano-structures

Abstract

The rise of technologically promising two-dimensional materials, particularly graphene, has further accelerated the already fast-paced progress in nano-synthesis techniques across all scales. While single atom devices are controllably manufactured, scalable techniques, such as chemical vapour deposition, have brought materials with tuneable nano-structures to the structural engineering scales. Hence, unprecedented design spaces for tailoring material properties at multiple, and previously unattainable, length scales have arisen and continue to expand.

Therefore, materials modelling communities must follow the integration of the physics, chemistry and synthesis fields, while accelerating their efforts towards an integrated virtual engineering design and simulation environment. The latter is of pivotal technological significance because future developments of novel materials and devices inherently require virtual designing and optimisation to remain economically feasible.

This work proposes and pursues a materials modelling landscape where state of the art methodologies are readily integrated across the scales. A mathematically rigorous molecular dynamics finite element, with novel theoretical attributes, is developed for readily implementing any MD force field, including reactive and fluctuating charge-dipole potentials, within an FEM-legacy numerical platform of solvers. Novel boundary conditions are presented for accurately capturing bending deformations in structures, discrete or continuum, which modularly achieve property homogenisation across differing scales and physical representations; thereby constituting an ideal bridging formulation for multi-scale and multi-physics integration. Numerical implementations of the proposed formulations are achieved within minutes using a network-theory-inspired code generator which presents novel strategies for meshing a priori unknown element topologies with motif-detection algorithms.

This work demonstrates the feasibility of an integrated modelling methodologies landscape and achieves a virtual engineering design and simulation environment, which is shown to be versatile and applicable from the smallest scales, for resolving the electromechanical behaviours in potential nano-device designs, to the larger scales where material nano-structures are virtually tested to deduce properties of engineering interest, such as graphenes fracture toughness.