Nonlinear Elasticity of Monolayer Graphene

Abstract

By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.

Interplay between bending and stretching in carbon nanoribbons

“…Nevertheless, even for such minor relaxations the energetics of the fully relaxed systems is expected to sizeably differ from the purely bended case, because of the extraordinary large value of the graphene Young modulus. 12 It is therefore important to provide a new estimation of the bending energy for the fully relaxed configurations.…”

“…Finally, this parametrization has been recently used for determining the nonlinear elastic moduli governing the graphene stretching elasticity. 12 The previous continuum analysis is useful both to create the input configurations for atomistic calculations and to define the simulation protocol. The investigated system consists in a nanoribbon formed by a perfect hexagonal carbon lattice, having width L in the range 4-12 nm and length l imposed to obtain a simulation box containing a constant number of ∼ 600 carbon atoms.…”

Dynamical polarization of graphene under strain

“…A linear dependence of δ on ε is justified in the elastic limit. Such an assumption is however quite robust, due to the extreme rigidity of graphene 18 , and is supported by ab initio calculations 19,21 .…”

“…Despite its quasi-two-dimensional character, it displays an exceptional tensile strength and stiffness 18 . In particular, recent ab initio calculations [19][20][21][22] as well as experiments 23 have demonstrated that graphene can sustain elastic deformations as large as 20%. The possibility of a straininduced semimetal-to-semiconductor transition, with the opening of a gap, has been therefore studied [24][25][26][27] .…”

Quantum effects in graphene monolayers: Path-integral simulations

“…Thus, there has been recently a rise of interest on thermodynamic properties of graphene, both theoretically and experimentally. [17][18][19][20] Finite-temperature properties of graphene have been studied by molecular dynamics and Monte Carlo simulations using ab-initio, [21][22][23] tight binding, [24][25][26][27] and empirical interatomic potentials. 5,[28][29][30][31][32] In most applications of these methods, atomic nuclei were described as classical particles.…”