Study and modeling of Graphene Structure using Finite Element Methods

New 2D materials (such as graphene) lead to a new class of 3D layered hybrid materials with controllably engineered atomic structures. Scalable processes (such as vapor deposition) have synthesized the majority of these meter-sized nanomaterials, offering many potential uses for next-generation structural graphene-based composites, electronics, sensors, DNA sequencing, or desalination membranes. It has many uses. Numerical design of nanomaterials and devices with various architectures and dimensions represents a distinct and increasingly important need, but requires the development of physically accurate and numerically efficient modeling approaches. Molecular dynamics (MD) can exhibit unfavorable numerical scaling, whereas more computationally expensive methods such as the continuum-based finite element method (FEM) show related discrete phenomena (such as fracture nucleation) There are inherent difficulties in capturing (i) We propose a molecular dynamics finite element method (MDFEM) for multiphysics and multiscale numerical design of nanomaterials. The MD equilibrium equations are embedded exactly within the computationally more versatile FEM. This MDFEM, shown to be equivalent to MD, readily implements any MD force field, including reactive and charge/dipole potentials, and was embedded in both standard explicit and implicit dynamic FEM codes, displaying linear computational scaling and a broader range of solver strategies and applicability (e.g. from femto-seconds to micro-meters); (ii) novel Objective Boundary Conditions (OBC), which account for non-local interactions with rotational period- icities of 1D/2D structures, and homogenise the response of discrete nano-systems for any continuum and structural idealisations of choice (e.g. plate theory). The proposed MDFEM and OBC were used to(i) design pillared graphene-based composite rein- forcement phases; (ii) obtain the latter's homogenised structural response; (iii) investigate the fracture toughness of cracked graphene; (iv) reduce numerical cost using its intrinsic suitability for concurrent multi-scale simulations of continuum and MD domains; (v) design multi-physics devices based on elec- tric field induced polarisations in Carbon Nanotubes (CNT) and porous graphene. Finally, the proposed MDFEM and OBC constitute a comprehensive framework for the virtual engineering design and tailoring of nano-material, structures and devices to target multi-functional properties, for a range of applications