An official website of the United States government
The buckling of thin elastic sheets is a classic mechanical instability that occurs over a wide range of scales. In the extreme limit of atomically thin membranes like graphene, thermal fluctuations can dramatically modify such mechanical instabilities. We investigate here the delicate interplay of boundary conditions, nonlinear mechanics, and thermal fluctuations in controlling buckling of confined thin sheets under isotropic compression. We identify two inequivalent mechanical ensembles based on the boundaries at constant strain (isometric) or at constant stress (isotensional) conditions. Remarkably, in the isometric ensemble, boundary conditions induce a novel long-ranged nonlinear interaction between the local tilt of the surface at distant points. This interaction combined with a spontaneously generated thermal tension leads to a renormalization group description of two distinct universality classes for thermalized buckling, realizing a mechanical variant of Fisher-renormalized critical exponents. We formulate a complete scaling theory of buckling as an unusual phase transition with a size-dependent critical point, and we discuss experimental ramifications for the mechanical manipulation of ultrathin nanomaterials.
more »
« less
Buckling mediated by mobile localized elastic excitations
Abstract Experiments reveal that structural transitions in thin sheets are mediated by the passage of transient and stable mobile localized elastic excitations. These “crumples” or “d-cones” nucleate, propagate, interact, annihilate, and escape. Much of the dynamics occurs on millisecond time scales. Nucleation sites correspond to regions where generators of the ideal unstretched surface converge. Additional stable intermediate states illustrate two forms of quasistatic inter-crumple interaction through ridges or valleys. These interactions create pairs from which extended patterns may be constructed in larger specimens. The onset of localized transient deformation with increasing sheet size is correlated with a characteristic stable crumple size, whose measured scaling with thickness is consistent with prior theory and experiment for localized elastic features in thin sheets. We offer a new theoretical justification of this scaling.
more »
« less
- Award ID(s):
- 2210797
- PAR ID:
- 10498314
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- PNAS Nexus
- Volume:
- 3
- Issue:
- 4
- ISSN:
- 2752-6542
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
If an adhesive is meant to be temporary, roughness often poses a challenge for design. An adhesive could be made soft so that it can deform and increase surface contact but a softer material will in general hold a smaller load. Bioinspired adhesives, made with numerous microscale posts, show promise as roughness tolerant adhesives but are complicated to fabricate. In this work, we show how thin polymer sheets, when crumpled into a roughly spherical shape, form a very simple and roughness tolerant adhesive system. We use micro and macro-scale experiments to measure adhesion forces between various substrates and crumpled polydimethylsiloxane sheets. We find the force-displacement curves resemble probe-tack experiments of traditional pressure sensitive adhesives and that moderate tensile forces are required to initiate interfacial failure. Notably, we see that sticky crumples often perform better on long wavelength roughness than they do on smooth substrates. In order to improve the peak pull-off forces, we create a sticky crumple from a thin sheet of a glassy polymer, polycarbonate, coated with an adhesive layer. This elasto-plastic sticky crumple achieves high pull-off forces even on the rough surface of a landscaping brick.more » « less
-
Abstract Onset of reconnection in the tail requires the current sheet thickness to be of the order of the ion thermal gyroradius or smaller. However, existing isotropic plasma models cannot explain the formation of such thin sheets at distances where the X‐lines are typically observed. Here we reproduce such thin and long sheets in particle‐in‐cell simulations using a new model of their equilibria with weakly anisotropic ion species assuming quasi‐adiabatic ion dynamics, which substantially modifies the current density. It is found that anisotropy/agyrotropy contributions to the force balance in such equilibria are comparable to the pressure gradient in spite of weak ion anisotropy. New equilibria whose current distributions are substantially overstretched compared to the magnetic field lines are found to be stable in spite of the fact that they are substantially longer than isotropic sheets with similar thickness.more » « less
-
Tunable piezoelectric metasurfaces have been proposed as a means of adaptively steering incident elastic waves for various applications in vibration mitigation and control. Bonding piezoelectric material to thin structures introduces electromechanical coupling, enabling structural dynamics to be altered via tunable electric shunts connected across each unit cell. For example, by carefully calibrating the inductive shunts, it is possible to implement the discrete phase shifts necessary for gradient-based waveguiding behaviors. However, experimental validations of localized phase shifting are challenging due to the narrow bandgap of local resonators, resulting in poor transmission of incident waves and high sensitivity to transient noise. These factors, in combination with the difficulties in experimental circuitry synthesis, can lead to significant variability of data acquired within the bandgap operating region. This paper presents a systematic approach for extracting localized phase shifts by taking advantage of the inherent correlation between the incident and transmitted wavefronts. During this procedure, matched filtering greatly reduces noise in the transmitted signal when operating in or near bandgap frequencies. Experimental results demonstrate phase shifts as large as −170° within the locally resonant bandgap, with an average 28% reduction in error relative to a direct time domain measurement of phase, enabling effective comparison of the dispersive behavior with corresponding analytical and finite element models. In addition to demonstrating the tunable waveguide characteristics of a piezoelectric metasurface, this technique can easily be extended to validate localized phase shifting of other elastic waveguiding metasurfaces.more » « less
-
Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on the notion that cell shape changes are induced by diffusible biomolecules that influence tissue contractility in a concentration-dependent manner – and whose concentration is in turn affected by the macroscopic tissue shape. We perform computational simulations of thin shell elastic dynamics to reveal propagating chemical and three-dimensional deformation patterns arising due to a sequence of buckling instabilities. Depending on the concentration threshold that actuates cell shape change, we find qualitatively different patterns. The mechanochemically coupled patterning dynamics are distinct from those driven by purely mechanical or purely chemical factors, and emerge even without diffusion. Using numerical simulations and theoretical arguments, we analyze the elastic instabilities that result from our model and provide simple scaling laws to identify wrinkling morphologies.more » « less
