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Related Concept Videos

Poisson's Ratio01:23

Poisson's Ratio

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

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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.
Bending of Members Made of Several Materials01:11

Bending of Members Made of Several Materials

In analyzing a structural member composed of two different materials with identical cross-sectional areas, it is crucial to understand how their distinct elastic properties affect the member's response under load. The analysis involves assessing stress and strain distributions using the transformed section concept, which accounts for variations in material properties.
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each material's...
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
Generalized Hooke's Law01:22

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...

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Automated Compression Testing of the Ocular Lens
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Automated Compression Testing of the Ocular Lens

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Negative Poisson's ratio materials via isotropic interactions.

Mikael C Rechtsman1, Frank H Stillinger, Salvatore Torquato

  • 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review Letters
|September 4, 2008
PubMed
Summary

Classical many-body systems under tension can exhibit auxetic behavior, meaning they get wider when stretched. This counterintuitive negative Poisson

Area of Science:

  • Condensed matter physics
  • Materials science
  • Classical mechanics

Background:

  • Poisson's ratio typically describes materials contracting laterally when stretched.
  • Auxetic materials exhibit counterintuitive negative Poisson's ratio.
  • Understanding auxetic behavior is crucial for designing novel materials.

Purpose of the Study:

  • To investigate the conditions under which classical many-body systems with isotropic pair interactions exhibit auxetic behavior.
  • To identify specific lattice structures that demonstrate a negative Poisson's ratio under tension.
  • To explore the role of interatomic potentials in achieving auxetic properties.

Main Methods:

  • Theoretical derivation of conditions for negative Poisson's ratio.
  • Analysis of lattice structures in two and three dimensions.

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  • Investigation using isotropic pair interactions and specific potentials like Lennard-Jones.

    • Main Results:

    • Demonstrated that crystalline systems under tension can exhibit a negative Poisson's ratio (auxetic behavior).
    • Derived conditions for auxeticity in two-dimensional triangular lattices and three-dimensional cubic lattices.
    • Showcased that Lennard-Jones potential can induce auxeticity in the triangular lattice.
    • Confirmed auxetic behavior in elastically isotropic cubic lattices.

    Conclusions:

    • Classical many-body systems with isotropic interactions can display auxetic properties.
    • Specific crystalline structures, like triangular and cubic lattices, are key to achieving negative Poisson's ratio.
    • The findings offer new insights into the mechanics of materials and potential for designing advanced materials.