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Related Experiment Videos

Tethered membranes far from equilibrium: buckling dynamics.

D Moldovan1, L Golubovic

  • 1Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

Solid membranes exhibit Euler buckling dynamics akin to phase ordering. Their wavelike patterns coarsen over time, revealing unique scaling behaviors distinct from other coarsening phenomena.

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Area of Science:

  • Solid mechanics
  • Materials science
  • Nonlinear dynamics

Background:

  • Classical Euler buckling describes the instability of compressed structures.
  • Phase ordering phenomena involve the coarsening of disordered systems into ordered domains.
  • Understanding the dynamics of compressed solid membranes is crucial for various engineering applications.

Purpose of the Study:

  • To investigate the dynamics of classical Euler buckling in compressed solid membranes.
  • To establish a relationship between membrane buckling dynamics and phase ordering phenomena.
  • To develop a theoretical framework for predicting the scaling behavior of membrane buckling.

Main Methods:

  • Analysis of the dynamics of compressed solid membranes undergoing Euler buckling.

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  • Relating membrane buckling dynamics to established principles of phase ordering.
  • Developing a scaling theory based on the morphology of evolving membranes, focusing on energy localization in ridges.
  • Deriving analytic estimates for coarsening exponents.

    • Main Results:

    • Membrane buckling dynamics were found to be analogous to phase ordering phenomena.
    • A wavelike pattern develops, with wavelength increasing as a power of time (coarsening).
    • Evolving membranes exhibit characteristics of growing interfaces, with transverse width increasing as a power of time.
    • A network of growing ridges, localizing elastic energy, was identified as a key morphological feature.
    • Analytic estimates for coarsening exponents were derived from the developed scaling theory.

    Conclusions:

    • The study establishes a novel connection between Euler buckling in solid membranes and phase ordering phenomena.
    • Membrane buckling dynamics display a distinct power-law scaling behavior, characterized by coarsening and growing interfaces.
    • The developed scaling theory provides valuable insights into the energy localization and morphological evolution of buckling membranes.