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Poisson's Ratio01:23

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Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign...
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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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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
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A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and...
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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Nonlinear Poisson Effect Governed by a Mechanical Critical Transition.

Jordan L Shivers1,2, Sadjad Arzash1,2, F C MacKintosh1,2,3

  • 1Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA.

Physical Review Letters
|February 8, 2020
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Summary
This summary is machine-generated.

Fiber networks show a large Poisson effect under strain, contracting significantly. This is due to a mechanical phase transition controlled by network connectivity, leading to critical phenomena in material behavior.

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Area of Science:

  • Materials Science
  • Mechanical Engineering
  • Physics

Background:

  • Fiber networks exhibit complex mechanical behaviors under deformation.
  • The Poisson effect describes a material's transverse strain in response to axial strain.
  • Anomalous mechanical responses in networks are not fully understood.

Purpose of the Study:

  • To investigate the mechanism behind the anomalously large and nonlinear Poisson effect in fiber networks.
  • To identify the critical factors controlling this phenomenon.
  • To characterize the associated mechanical phase transition.

Main Methods:

  • Applying extensional strain to fiber networks.
  • Measuring transverse contraction and volume reduction.
  • Analyzing the relationship between strain, network connectivity, and mechanical response.
  • Observing critical signatures like Poisson's ratio peaks and nonaffine strain fluctuations.

Main Results:

  • Fiber networks demonstrate a dramatic transverse contraction and volume reduction at low applied strains.
  • A collective mechanical phase transition governs this Poisson effect.
  • The critical strain for this transition is dependent on network connectivity.
  • Anomalous peaks in Poisson's ratio and diverging nonaffine strain fluctuations were observed.

Conclusions:

  • The anomalous Poisson effect in fiber networks is a result of a critical mechanical phase transition.
  • Network connectivity plays a crucial role in determining the critical strain for this transition.
  • The findings provide insights into the mechanics of disordered materials and critical phenomena.