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Related Concept Videos

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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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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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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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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In designing structural elements and machine parts using ductile materials, it is crucial to ensure that these components withstand applied stresses without yielding. Yielding is initially determined through a tensile test, which evaluates the material's response to uniaxial stress. However, tensile stress is insufficient when components face biaxial or plane stress conditions This condition requires advanced criteria to predict failure.
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Related Experiment Video

Updated: Jan 8, 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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Material-defined two-dimensional numerical model for grain-scale nonlinear elasticity.

Ryley G Hill1, Robert A Guyer1,2, Paul A Johnson1

  • 1Earth and Environmental Sciences 17, National Security Earth Science, Los Alamos National Laboratory, New Mexico 87545, USA.

The Journal of the Acoustical Society of America
|December 23, 2025
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Summary
This summary is machine-generated.

This study models nonlinear elastic wave behavior in granular media using Berea Sandstone properties. The microstructural model explains experimentally observed acoustic nonlinearity in solids.

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Area of Science:

  • Geophysics
  • Materials Science
  • Acoustics

Background:

  • Characterizing complex granular media requires understanding nonlinear mesoscopic elastic materials.
  • Acoustic manifestations are key to this characterization.

Purpose of the Study:

  • To develop a numerical model for nonlinear elastic wave behavior in granular media.
  • To capture the behavior of Berea Sandstone under cyclic loading.

Main Methods:

  • Developed a numerical model using Berea Sandstone properties.
  • Simulated quasi-static loading scenarios.
  • Tracked the material matrix to identify force pairs controlling hysteresis.

Main Results:

  • The model captures nonlinear elastic wave behavior and rate-independent hysteresis.
  • Spatially varying nonlinear stress-strain behavior in the matrix governs hysteresis.
  • Identified force pairs consistent with phenomenological models.

Conclusions:

  • Physically motivated microstructural modeling provides insight into experimentally observed nonlinear acoustic phenomena.
  • This approach advances understanding beyond phenomenological descriptions of acoustic nonlinearity in solids.