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Related Concept Videos

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

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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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Bending of Members Made of Several Materials

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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.
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Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
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Hooke's Law

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Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.
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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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Unveiling Extreme Anisotropy in Elastic Structured Media.

G Lefebvre1, T Antonakakis2, Y Achaoui3

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Physical Review Letters
|July 12, 2017
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Summary
This summary is machine-generated.

Researchers experimentally confirmed a theory predicting a switch in material properties for elastic waves. This allows for precise control over wave behavior by shifting the frequency, leading to distinct anisotropic modes.

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Area of Science:

  • Physics
  • Materials Science
  • Wave Phenomena

Background:

  • Periodic structures exhibit unique properties at symmetry points, like zero group velocity and Dirac cones.
  • Analyzing these properties from dispersion surfaces is challenging, especially in 3D or at high frequencies.
  • Asymptotic high-frequency homogenization theory offers a new predictive approach.

Purpose of the Study:

  • To experimentally validate a recently proposed asymptotic high-frequency homogenization theory.
  • To investigate the behavior of elastic waves in a pinned metallic plate.
  • To demonstrate precise wave control through frequency manipulation.

Main Methods:

  • Application of asymptotic high-frequency homogenization theory.
  • Time-domain experimental analysis of elastic waves.
  • High-frequency spectral region analysis of effective medium tensor.

Main Results:

  • Experimental confirmation of a narrow high-frequency spectral region with a dramatic switch in the effective medium tensor (positive definite to indefinite).
  • Observation of two distinct, highly anisotropic wave modes resulting from a small frequency shift.
  • Validation of the underlying effective equation's change in form (elliptic to hyperbolic).

Conclusions:

  • The study confirms the predictive power of the asymptotic homogenization theory for wave phenomena in periodic structures.
  • Precise control over elastic wave behavior is achievable by manipulating frequency within specific spectral regions.
  • The findings highlight the importance of effective predictive models for designing advanced wave control devices.