Thermal fluctuations and effective bending stiffness of elastic thin sheets and graphene: A nonlinear analysis

Fatemeh Ahmadpoor, Peng Wang, Rui Huang, Pradeep Sharma

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


The study of statistical mechanics of thermal fluctuations of graphene—the prototypical two-dimensional material—is rendered rather complicated due to the necessity of accounting for geometric deformation nonlinearity. Unlike fluid membranes such as lipid bilayers, coupling of stretching and flexural modes in solid membranes like graphene leads to a highly anharmonic elastic Hamiltonian. Existing treatments draw heavily on analogies in the high-energy physics literature and are hard to extend or modify in the typical contexts that permeate materials, mechanics and some of the condensed matter physics literature. In this study, using a variational perturbation method, we present a “mechanics-oriented” treatment of the thermal fluctuations of elastic sheets such as graphene and evaluate their effect on the effective bending stiffness at finite temperatures. In particular, we explore the size, pre-strain and temperature dependency of the out-of-plane fluctuations, and demonstrate how an elastic sheet becomes effectively stiffer at larger sizes. Our derivations provide a transparent approach that can be extended to include multi-field couplings and anisotropy for other 2D materials. To reconcile our analytical results with atomistic considerations, we also perform molecular dynamics simulations on graphene and contrast the obtained results and physical insights with those in the literature.

Original languageEnglish (US)
Pages (from-to)294-319
Number of pages26
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Oct 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


  • Graphene
  • Nonlinear elasticity
  • Thermal fluctuations
  • Variational perturbation method


Dive into the research topics of 'Thermal fluctuations and effective bending stiffness of elastic thin sheets and graphene: A nonlinear analysis'. Together they form a unique fingerprint.

Cite this