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Related Concept Videos

Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

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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Plastic Behavior

A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and reloaded.
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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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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Published on: April 25, 2019

Nonlinear elastic stress response in granular packings.

Brian P Tighe1, Joshua E S Socolar

  • 1Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary

This study reveals how nonlinear elastic responses differ between isotropic and hexagonal granular materials under localized forces. Nonlinearities enhance stress propagation, especially in hexagonal materials.

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Area of Science:

  • * Physics of granular materials
  • * Nonlinear elasticity
  • * Continuum mechanics

Background:

  • * Classical Boussinesq theory describes stress in linear, isotropic materials.
  • * Continuum theory breaks down at scales comparable to grain size.
  • * Granular materials exhibit complex responses to localized forces.

Purpose of the Study:

  • * To investigate nonlinear elastic responses in 2D granular materials.
  • * To understand differences between isotropic and hexagonal anisotropy.
  • * To model the breakdown of continuum theory at small scales.

Main Methods:

  • * Developed power series corrections to Boussinesq theory.
  • * Modeled continuum breakdown using phenomenological multipole parameters.
  • * Fitted theoretical framework to experimental data from Geng (2001).

Main Results:

  • * Framework successfully fits data for both isotropic and hexagonal packings.
  • * Hexagonal packings require stronger anisotropic elastic coefficients than simple models.
  • * Induced dipole and quadrupole terms cause stress propagation away from the vertical.

Conclusions:

  • * Nonlinearities significantly enhance stress propagation scale in hexagonal materials.
  • * The study provides a framework for understanding anisotropic granular material behavior.
  • * Findings highlight the importance of nonlinear effects and anisotropy in granular systems.