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Patterns from scale-free instabilities in soft solids

Evan Hohlfeld (UMass Amherst)

Soft Materials and Structures

Mon 10:45 - 12:15

Barus-Holley 158

Short wavelength instabilities in continua, e.g. the crumpling of an elastic membrane, or the Rayleigh-Taylor or Kelvin-Helmholz instabilities of fluids interfaces, can produce complex and intricate patterns. The thresholds for these instabilities typically vanish with the surface tension or other microscopic parameter, making them intrinsically supercritical. In 1965 M. A. Biot predicted that solids have a host of scale-free linear instabilities that set in at at finite strain. This raises the possibility of a subcritical scale free instability. Recently, two of Biot's instabilities---at a free surface and at an interface---were shown to be deeply subcritical, and to result in the nucleation and growth of sharply creased interfacial folds called sulci (E. Hohlfeld and L. Mahadevan, Phys. Rev. Lett. 106, 105702 (2011)). I will explain how these instabilities and their resulting patterns can be quantitatively explained in terms of a new kind of nonlinear, scale-free critical point which is invisible to linearization. I will also discuss the prospects that similar a critical points may lurk behind Biot's other instabilities.