Nonlinear Mechanics of Single-Atomic-Layer Graphene Sheets

Abstract

The unique lattice structure and properties of graphene has drawn tremendous interests recently.By combining continuum and atomistic approaches, this paper investigates the mechanical properties of single-atomic-layer graphene sheets. A theoretical framework of nonlinear continuum mechanics is developed for graphene under both in-plane and bending deformation.Atomistic simulations are carried out to deduce the effective mechanical properties. It is found that graphene becomes highly nonlinear and anisotropic under finite-strain uniaxial stretch, and coupling between stretch and shear occurs except for stretching in the zigzag and armchair directions. The theoretical strength (fracture strain and fracture stress) of perfect graphene lattice also varies with the chiral direction of uniaxial stretch. By rolling graphene sheets into cylindrical tubes of various radii, the bending modulus of graphene is obtained. Buckling of graphene ribbons under uniaxial compression is simulated and the critical strain for the onset of buckling is compared to a linear buckling analysis.

Stretch-induced softening of bending rigidity in graphene

“…8,9 It is known that wrinkling of a thin elastic sheet depends strongly on both the bending stiffness and stretching, 10 and controllable ripples in suspended graphene have indeed been created via in-plane stretching. 11 The behavior of graphene under uniaxial stretching has been studied by molecular mechanics simulations [12][13][14][15] and first-principle calculations. [16][17][18][19][20][21] The bending stiffness of graphene has also been studied through theoretical 12,13,[22][23][24][25] and first-principle calculations.…”

“…11 The behavior of graphene under uniaxial stretching has been studied by molecular mechanics simulations [12][13][14][15] and first-principle calculations. [16][17][18][19][20][21] The bending stiffness of graphene has also been studied through theoretical 12,13,[22][23][24][25] and first-principle calculations. [26][27][28] However, the coupling between bending and stretching, in particular the bending stiffness of graphene in a stretched state, has not been reported in the literature.…”

“…13,22,[24][25][26][27][28] In standard approach, fully relaxed graphene sheets are rolled into a set of cylindrical nanotubes with different radii. The strain energy density of these tubes can be expressed as U ¼ D 2R 2 , where D is the bending stiffness of graphene and R is the tube radius.…”

Non-linear elastic moduli of Graphene sheet-reinforced polymer composites

“…Therefore, theoretical and numerical studies have been developed based on the atomistic simulation at nano-scale and continuum/structural mechanics modelling. These studies deal essentially with quantum mechanics (QM) calculations for instance in Wei et al (2009) Lu and Huang (2009). Under large deformations, the elastic behaviour of the Graphene sheet must be considered non-linear.…”

I-V characteristics of in-plane and out-of-plane strained edge-hydrogenated armchair graphene nanoribbons

“…There is an increasing interest in examining their mechanical [36][37][38][39][40][41][42][43][44][45][46][47] and electronic properties [48][49][50][51][52][53][54][55][56][57][58] under different constrains such as tensile stress to predict the behavior of future possible devices. Particularly, strain studies on graphene nanoribbons are gaining much attention as the control of their mechanical deformation could allow the creation of novel devices for energy harvesting [83][84][85][86] .…”