This paper reviews the mechanical properties of graphene with particular attention to what is established and what is still uncertain. It clarifies the thickness and the elastic constants, and by also considering also phonon frequencies, it argues that “best values” come from graphite, when available. Properties not available from graphite include bending stiffness; this can be determined from studies of carbon nanotubes as well as graphene. In many ways, nanotubes provide access to fundamental properties of graphene, not least because they are the only form of graphene that can be unsupported (unstrained) in vacuum. Environmental effects are considered, including both interactions with substrates and with other solid and liquid media, which may affect the geometrical parameters defining graphene and associated elastic constants. Major uncertainties persist whether slipping or sticking dominates experimental observation, both between graphene and solid media, and between the layers of bilayer and multilayer graphene. The paper concludes with a short discussion of continuum and atomistic models of graphene.

This review explores recent advances in the mechanical reinforcement of polymer nanocomposites using 2D nanofillers, focusing on the mechanisms of reinforcement, evaluation of model and bulk nanocomposites, and the effects of hybrid filler combinations.

Straintronics leverages mechanical strain to alter the electronic properties of materials, providing an energy-efficient alternative to traditional electronic controls while enhancing device performance. Key to the application of straintronics is bandgap engineering, which enables tuning of the energy difference between the valence and conduction bands of a material to optimize its optoelectronic properties. This mini-review highlights the fundamental principles of straintronics and the critical role of bandgap engineering within this context. It discusses the unique characteristics of various two-dimensional (2D) materials, such as graphene, transition metal dichalcogenides (TMDs), hexagonal boron nitride (h-BN), and black phosphorus, which make them suitable for strain-engineered applications. Detailed examples of how mechanical deformation can modulate the bandgap to achieve desired electronic properties are provided, while recent experimental and theoretical studies demonstrating the mechanisms by which strain influences the bandgap in these materials are reviewed, emphasizing their implications for device fabrication. The review concludes with an assessment of the challenges and future directions in the development of high-performing straintronic devices, highlighting their potential applications in flexible electronics, sensors, and optoelectronics.

This work addresses a fundamental question: To what extent is graphene graphite? In particular does 2D graphene have many of the same 3D mechanical properties as graphite, such as the bulk modulus and elastic constant $c_{33}$? We have obtained, for the first time, unambiguous Raman spectra from unsupported monolayer graphene under pressure. We have used these data to quantify the out-of-plane stiffness of monolayer graphene, which is hard to define due to its 2D nature. Our data indicate a first physically meaningful out-of-plane stiffness of monolayer graphene, and find it to be consistent with that of graphite. We also report a shift rate of the in-plane phonon frequency of unsupported monolayer graphene to be $5.4{\mathrm{cm}}^{-1}{\mathrm{GPa}}^{-1}$, very close to that of graphite ($4.7{\mathrm{cm}}^{-1}{\mathrm{GPa}}^{-1}$), contrary to the previous value for supported graphene. Our results imply that monolayer graphene has similar in-plane and out-of-plane stiffnesses, and anharmonicities to graphite.