Advances in finite element modelling of graphene and associated nanostructures

Graphene and its associated nanostructures (GANS) have been widely investigated by means of experimental and numerical approaches over the last decade. GANS and GANS reinforced composite materials show exceptional promise towards superior mechanical and thermal properties along with limitless opportunity to tailor, control, design, modify and manipulate such properties. These attributes make graphene and its associated nanostructures as one of the most important future material technologies in aerospace, automotive, medical, civil and military sectors of the 21st century. Among the various numerical methods used to analyse GANS and GANS reinforced composite materials, the finite element method (FEM) plays a prominent role. The FEM has been the standard analysis and simulation method for conventional structural and mechanical problems over the past half a century. However, its growing role and impact in atomistic-scale numerical simulation in general, and GANS, in particular, is not well known within the wider scientific and engineering modelling and simulation research community. There is a compelling need to document the expansive use of the finite element method, its advantages, shortcomings, relevance and purpose in a way which is pertinent to both material science and numerical simulation researchers. This paper serves this need by discussing the current state of the art of finite element methodologies available to study GANS and GANS reinforced composites in the most comprehensive manner. A detailed description of the popular space frame based numerical simulation strategy widely used to represent GANS is given. An extensive survey is conducted on more than 600 research papers in order to examine the finite element predictions of the mechanical and thermal properties of graphene and its associated composite materials. These properties are selected in view of their direct relevance to crucial future technologies, such as high-performance automotive components, aerospace and bioengineering systems, energy technologies, and advanced therapeutic and surgical devices. Omissions of some fundamental mechanical and thermal modelling issues for GANS have been identified and insightful guidance towards future research directions to comprehensively address them is given. By reviewing a significant breadth of publications across several academic disciples, a large scatter in the numerical predictions of essential material constants arising from the differences in fundamental assumptions and approximations has been reported. The origin of such discrepancies has been identified, analysed and established. The paper further focuses on the idealization of nanostructures and nanocomposites by means of representative volume elements (RVEs). The need for this multiscale modelling strategy to mature in order to include the simultaneous description of different material length scales within multiphysics simulation problems has been discussed. This paper will serve as standalone reference material for future research works and will pave the way for novel investigations in the context of atomistic simulations and their potential applications to the development of next-generation engineering devices and cutting-edge technological applications.