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Related Concept Videos

Elasticity01:12

Elasticity

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Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
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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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Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

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Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...
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Strain and Elastic Modulus01:15

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The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear...
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Elasticity in Concrete01:20

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Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear...
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Quantum Critical Elasticity.

Mario Zacharias1, Indranil Paul2, Markus Garst1

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Summary
This summary is machine-generated.

Quantum critical elasticity in atomic crystal lattices leads to unique phonon behaviors and violates standard thermodynamic laws. This phenomenon is crucial for understanding quantum phase transitions in certain advanced materials.

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Area of Science:

  • Condensed matter physics
  • Materials science
  • Quantum mechanics

Background:

  • Atomic crystal lattices exhibit elastic instabilities at zero temperature.
  • Long-range shear forces influence phonon behavior during these transitions.
  • Critical phonon fluctuations can be suppressed to lower dimensional manifolds.

Purpose of the Study:

  • To investigate elastic instabilities in atomic crystal lattices at zero temperature.
  • To explore the resulting phonon thermodynamics and critical behavior.
  • To connect these phenomena to quantum phase transitions in specific materials.

Main Methods:

  • Analysis of phonon velocities and their vanishing points.
  • Characterization of critical phonon fluctuations.
  • Investigation of symmetry-breaking elastic transitions and their thermodynamic consequences.

Main Results:

  • Phonon velocities vanish along specific crystallographic directions.
  • Critical phonon fluctuations are governed by a Gaussian fixed point.
  • Symmetry-breaking transitions lead to thermodynamics violating Debye's T(3) law for specific heat.

Conclusions:

  • Quantum critical elasticity is triggered by soft modes coupling linearly to the strain tensor.
  • This is relevant for electronic Ising-nematic quantum phase transitions in tetragonal crystals.
  • Findings apply to materials like cuprates, ruthenates, and iron-based superconductors.