2. INTRODUCTION
Since the first successful synthesis of graphene just over a decade ago, a variety of two-dimensional (2D)
materials (e.g., transition metal-dichalcogenides, hexagonal boron-nitride, etc.) have been discovered. Among the
many unique and attractive properties of 2D materials, mechanical properties play important roles in
manufacturing, integration and performance for their potential applications. Mechanics is indispensable in the
study of mechanical properties, both experimentally and theoretically. The coupling between the mechanical and
other physical properties (thermal, electronic, optical) is also of great interest in exploring novel applications,
where mechanics has to be combined with condensed matter physics to establish a scalable theoretical
framework. Moreover, mechanical interactions between 2D materials and various substrate materials are essential
for integrated device applications of 2D materials, for which the mechanics of interfaces (adhesion and friction)
has to be developed for the 2D materials. Here we review recent theoretical and experimental works related to
mechanics and mechanical properties of 2D materials. While graphene is the most studied 2D material to date, we
expect continual growth of interest in the mechanics of other 2D materials beyond graphene
3. (A) Force-displacment data from AFM nanoindentaiton of suspended monolayer
graphene, with different tip radii and specimen diameters; fracture loads are
indicated by ? marks. (B) Force-displacement data measured by
nanoindentaiton of suspended mica nanosheets of 2, 6 and 12 atomic layers.
(Inset) schematic diagram of the indentation experiment.
5. (A) Decreasing ripple amplitude under increasing tensile strain; (B) Tangent modulus of graphene at a finite
temperature (T = 300 K).
6. Vacancy configurations in 2D materials: (A) graphene, (B) MoS 2 (Mo
purple and S yellow), and (C) phosphorene.
7. Grain boundaries in 2D materials: (A) graphene, (B) MoS 2 , the left red is Mo-rich, the right blue is S-rich [96]; and (C)
phosphorene, where one still can recognize the strongly-puckered.
8. Toughening mechanisms in 2D materials. (A-C) Observed mechanisms of toughness enhancement due to topological defects in
graphene [169]. (D) Highly stretchable graphene kirigami [9]. (E) MD simulation snapshots for stress distribution in a stretched
graphene kirigami [175]. (F) Flaw insensitive fracture in a nanocrystalline graphene sample [153]. (G) Transition from catastrophic to
localized failure with increasing defect content [183]. Figures adapted from: (A-C) [169], (D) [9], (E) [175], (F) [153], and (G) [183].
9. (A) (left) STM images of a graphene monolayer patch on Pt(111) with four nanobubbles at the graphene-Pt border and one in the
patch interior. (right) Topography of theoretically simulated graphene nanobubble with calculated pseudomagnetic field distribution.
(B) Distribution of the pseudomagnetic field in a graphene under equi-triaxial tension. (C) Subject to uniaxial tension, a suitably
patterned graphene
10.
11. Compilation of measured adhesion energy values for 1 to 5-layer graphene membranes ( 1 5 n ? ) [26, 274, 278]. Each
symbol represents a different flake. The points with the error bars represent adhesion energies from the center post of
the island blister test [278].
