A comprehensive lattice-stability limit surface for graphene
Author(s)
Kumar, Sandeep; Parks, David Moore
DownloadParks_A comprehensive.pdf (5.343Mb)
PUBLISHER_CC
Publisher with Creative Commons License
Creative Commons Attribution
Terms of use
Metadata
Show full item recordAbstract
The limits of reversible deformation in graphene under various loadings are examined using lattice-dynamical stability analysis. This information is then used to construct a comprehensive lattice-stability limit surface for graphene, which provides an analytical description of incipient lattice instabilities of all kinds, for arbitrary deformations, parametrized in terms of symmetry-invariants of strain/stress. Symmetry-invariants allow obtaining an accurate parametrization with a minimal number of coefficients. Based on this limit surface, we deduce a general continuum criterion for the onset of all kinds of lattice-stabilities in graphene: an instability appears when the magnitude of the deviatoric strain γ reaches a critical value γ c which depends upon the mean normal strain E¯ and the directionality θ of the principal deviatoric stretch with respect to reference lattice orientation. We also distinguish between the distinct regions of the limit surface that correspond to fundamentally different mechanisms of lattice instabilities in graphene, such as structural versus material instabilities, and long-wave (elastic) versus short-wave instabilities. Utility of this limit surface is demonstrated in assessment of incipient failures in defect-free graphene via its implementation in a continuum finite elements analysis (FEA). The resulting scheme enables on-the-fly assessments of not only the macroscopic conditions (e.g., load and deflection) but also the microscopic conditions (e.g., local stress/strain, spatial location, temporal proximity, and nature of incipient lattice instability) at which an instability occurs in a defect-free graphene sheet subjected to an arbitrary loading condition. Keywords
Graphene
Ideal strength
Lattice-stability limits
Finite element analysis
Date issued
2015-10Department
Massachusetts Institute of Technology. Department of Mechanical EngineeringJournal
Journal of the Mechanics and Physics of Solids
Publisher
Elsevier
Citation
Kumar, Sandeep, and Parks, David M. “A Comprehensive Lattice-Stability Limit Surface for Graphene.” Journal of the Mechanics and Physics of Solids 86 (January 2016): 19–41 © 2015 Elsevier Ltd
Version: Original manuscript
ISSN
0022-5096