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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Nonlinear elastic response in solid helium: critical velocity or strain?

James Day1, Oleksandr Syshchenko, John Beamish

  • 1Department of Physics, University of Alberta, Edmonton, Alberta, T6G 2G7, Canada.

Physical Review Letters
|April 7, 2010
PubMed
Summary

Experiments reveal mass decoupling in solid helium-4 (4He), indicating a critical velocity for supersolidity. This phenomenon, observed in both torsional oscillators and shear modulus measurements, is linked to dislocation motion.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials

Background:

  • Solid helium-4 (4He) exhibits exotic quantum phenomena, including supersolidity.
  • Previous torsional oscillator experiments suggested mass decoupling and a critical velocity associated with supersolidity.

Purpose of the Study:

  • To investigate the amplitude dependence of the elastic shear modulus in solid 4He.
  • To differentiate between velocity-dependent and displacement-dependent amplitude effects.
  • To understand the underlying mechanisms of mass decoupling in solid 4He.

Main Methods:

  • Measurement of the elastic shear modulus across a wide frequency range.
  • Utilizing torsional oscillator experiments to probe mass decoupling.
  • Analysis of the shear modulus's dependence on stress and velocity.

Main Results:

  • Observed amplitude-dependent behavior in the elastic shear modulus, mirroring torsional oscillator findings.
  • Demonstrated that the shear modulus's amplitude dependence is primarily stress-driven, not velocity-driven.
  • Identified a critical stress for the breakaway of weakly pinned dislocations.

Conclusions:

  • The observed mass decoupling in solid 4He is attributed to the motion of dislocations.
  • Dislocations, weakly pinned by helium-3 (3He) impurities, become mobile under sufficient stress, leading to supersolid behavior.
  • The stress-dependent nature of the shear modulus provides crucial insights into the dynamics of dislocations in solid 4He.