4.8 Article

Spontaneous Tilt of Single-Clamped Thermal Elastic Sheets

期刊

PHYSICAL REVIEW LETTERS
卷 128, 期 2, 页码 -

出版社

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.128.028006

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资金

  1. National Science Foundation [NSF PHY-1748958, CNS-1725797]
  2. National Natural Science Foundation of China [11904265]
  3. Hubei Provincial Natural Science Foundation [2020CFB670]
  4. Fundamental Research Funds for the Central Universities [2042020kf0033]
  5. California NanoSystems Institute
  6. Materials Research Science and Engineering Center (MRSEC) at UC Santa Barbara [NSF DMR 1720256]

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Even at zero temperature, very thin elastic sheets exhibit nonlinear elastic response. Molecular dynamics simulations reveal a tilted phase where the sheet fluctuates about a mean configuration inclined with respect to the horizontal. A model is developed to predict the tilted and untilted regions in the phase diagram. These findings have significant implications for two-dimensional mechanical metamaterials.
Very thin elastic sheets, even at zero temperature, exhibit nonlinear elastic response by virtue of their dominant bending modes. Their behavior is even richer at finite temperature. Here, we use molecular dynamics to study the vibrations of a thermally fluctuating two-dimensional elastic sheet with one end clamped at its zero-temperature length. We uncover a tilted phase in which the sheet fluctuates about a mean configuration inclined with respect to the horizontal, thus breaking reflection symmetry. We determine the phase behavior as a function of the aspect ratio of the sheet and the temperature. We show that tilt may be viewed as a type of transverse buckling instability induced by clamping coupled to thermal fluctuations and develop an analytic model that predicts the tilted and untilted regions of the phase diagram. Qualitative agreement is found with the molecular dynamics simulations. Unusual response driven by control of purely geometric quantities like the aspect ratio, as opposed to external fields, offers a very rich playground for two-dimensional mechanical metamaterials.

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