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Surface tension can destabilize elastic cylinders, causing them to phase-separate into segments with different stretches. This phenomenon, governed by a critical surface tension threshold, explains infinite wavelength instability and hysteresis in stretched materials.

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Area of Science:

  • Materials Science
  • Solid Mechanics
  • Soft Matter Physics

Background:

  • Elastic cylinders can become unstable under sufficient surface tension.
  • Understanding the energy landscape of stretched cylinders is crucial for predicting instability.

Purpose of the Study:

  • To explain the infinite wavelength instability of elastic cylinders due to surface tension.
  • To model the phase separation and hysteresis loop of a stretched elastic cylinder.

Main Methods:

  • Analysis of the cylinder's energy function E(λ) under longitudinal stretch λ.
  • Application of a Maxwell construction to identify phase separation.
  • Nonlinear finite-element calculations for verification.

Main Results:

  • Surface tension (Γ) exceeding a threshold (sqrt[32]) causes the energy function to lose convexity.
  • Cylinders phase-separate into two segments with stretches λ₁ and λ₂.
  • Instability exhibits a subcritical hysteresis loop with constant amplitude and tension.

Conclusions:

  • The model successfully explains infinite wavelength instability and predicts hysteresis.
  • Finite-element analysis confirms theoretical predictions and characterizes phase interfaces.
  • A new length scale emerges near the instability threshold, enabling an effective 1D theory.