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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

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.
Plastic Behavior01:21

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.
Hooke's Law01:26

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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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Shearing Strain

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...
Strain and Elastic Modulus01:15

Strain and Elastic Modulus

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...
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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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Related Experiment Video

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Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
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Published on: January 18, 2022

Incremental stress-strain relation from granular elasticity: comparison to experiments.

Yimin Jiang1, Mario Liu

  • 1Theoretische Physik, Universität Tübingen, Tübingen, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed
Summary

Granular materials behave elastically under small stress changes. This study validates an elastic stress-strain model against experimental data, confirming its accuracy for granular media analysis.

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Area of Science:

  • Geotechnical Engineering
  • Materials Science
  • Physics of Granular Media

Background:

  • Granular materials exhibit complex mechanical behaviors.
  • Elasticity and reversibility are key characteristics under specific conditions.
  • Previous models for static stress distributions exist.

Purpose of the Study:

  • To evaluate an elastic stress-strain relation for granular media.
  • To compare theoretical predictions with experimental incremental stress-strain data.
  • To provide a more robust foundation for the yield condition in granular mechanics.

Main Methods:

  • Utilizing a previously established elastic stress-strain relationship.
  • Comparing model predictions with experimental results from Kuwano and Jardine (2002).
  • Analyzing incremental stress-strain behavior.

Main Results:

  • The elastic stress-strain relation shows satisfactory agreement with experimental data.
  • The model accurately predicts incremental stress-strain responses in granular media.
  • The study strengthens the understanding and application of the yield condition.

Conclusions:

  • The elastic model is a reliable tool for analyzing granular media under small stress increments.
  • Experimental validation supports the use of this model for predicting material behavior.
  • Further refinement of the yield condition for granular materials is supported.