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Related Concept Videos

Shearing Strain01:20

Shearing Strain

1.9K
The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
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Three-Dimensional Analysis of Strain01:29

Three-Dimensional Analysis of Strain

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Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
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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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Structures of Solids02:22

Structures of Solids

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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Generalized Hooke's Law01:22

Generalized Hooke's Law

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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...
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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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Related Experiment Video

Updated: May 7, 2026

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
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Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

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Shear localization in three-dimensional amorphous solids.

Ratul Dasgupta1, Oleg Gendelman, Pankaj Mishra

  • 1Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 16, 2013
PubMed
Summary
This summary is machine-generated.

This study extends shear localization theory to 3D amorphous solids, revealing a fundamental plastic instability explained by a lattice of inclusions. This lattice forms at a 45-degree angle to stress, predicting a yield-strain threshold for stability.

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Last Updated: May 7, 2026

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Condensed Matter Physics

Background:

  • Shear localization in 2D amorphous solids involves displacement quadrupoles at 45 degrees to stress.
  • Extending this theory to three dimensions is crucial for understanding material failure.

Purpose of the Study:

  • To extend the theory of shear localization from 2D to 3D amorphous solids.
  • To explain the fundamental plastic instability in 3D under shear stress.

Main Methods:

  • Theoretical extension of 2D shear localization models to 3D.
  • Analysis of plastic instability through the formation of anisotropic elastic inclusions.
  • Numerical simulations to validate theoretical predictions.

Main Results:

  • The 3D plastic instability is characterized by a 2D triangular lattice of elementary events.
  • This lattice is oriented on a plane at 45 degrees to the principal stress axis.
  • A yield-strain threshold, dependent on material parameters and Poisson ratio, is identified for energetic favorability.

Conclusions:

  • The 3D theory accurately predicts shear localization phenomena.
  • The lattice structure provides a unified explanation for instability in both 2D and 3D.
  • The findings offer insights into the mechanical behavior of amorphous solids.