Abstract
A long elastic cylinder, with radius and shear-modulus , becomes unstable given sufficient surface tension . We show this instability can be simply understood by considering the energy, , of such a cylinder subject to a homogenous longitudinal stretch . Although has a unique minimum, if surface tension is sufficient it loses convexity in a finite region. We use a Maxwell construction to show that, if stretched into this region, the cylinder will phase-separate into two segments with different stretches and . Our model thus explains why the instability has infinite wavelength and allows us to calculate the instability's subcritical hysteresis loop (as a function of imposed stretch), showing that instability proceeds with constant amplitude and at constant (positive) tension as the cylinder is stretched between and . We use full nonlinear finite-element calculations to verify these predictions and to characterize the interface between the two phases. Near the length of such an interface diverges, introducing a new length scale and allowing us to construct a one-dimensional effective theory. This treatment yields an analytic expression for the interface itself, revealing that its characteristic length grows as .
- Received 13 January 2017
DOI:https://doi.org/10.1103/PhysRevE.95.053106
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