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Related Concept Videos

Plasticity00:58

Plasticity

Plasticity is the property where an object loses its elasticity and undergoes irreversible deformation, even after the deformation forces are eliminated. If a material deforms irreversibly without increasing stress or load, then this is called ideal plasticity. For example, when a force is applied to an aluminum rod, it changes its shape, but it does not return to its original shape once the force is removed. Plastic deformation or ductility is thus a permanent deformation or change in the...
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.
Circular Shafts - Elastoplastic Materials01:24

Circular Shafts - Elastoplastic Materials

The study of solid circular shafts under stress shows that within the elastic limit, stress increases directly to the distance from the shaft's center. This relationship holds until the shaft reaches a critical point of stress, beyond which it begins to yield, marking the transition from elastic to plastic deformation. At this crucial juncture, the maximum torque the shaft can endure without permanent deformation is determined, signifying the limit of its elastic behavior.
As torque on the...
Plastic Deformations01:14

Plastic Deformations

It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...
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 Deformations

Plastic deformation represents a fundamental concept in materials science, which explains the irreversible change in the shape of a material when it experiences stress beyond its elastic capability. This phenomenon is important in structural engineering, especially in designing and analyzing cantilever beams—structures that are securely fixed at one end and bear loads at the opposite end. When these beams are subjected to loads within their elastic range, they will return to their original...

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Environmentally-controlled Microtensile Testing of Mechanically-adaptive Polymer Nanocomposites for ex vivo Characterization
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Published on: August 20, 2013

Force chains, microelasticity, and macroelasticity.

C Goldenberg1, I Goldhirsch

  • 1School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel. chayg@post.tau.avc.il

Physical Review Letters
|August 23, 2002
PubMed
Summary

Granular and nanoscale materials show elasticity deviations at small scales, disappearing as size increases. Models reveal force chains and stress distributions consistent with experiments, validating findings across different scales.

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Area of Science:

  • Physics
  • Materials Science
  • Mechanical Engineering

Background:

  • Quasistatic granular materials and nanoscale materials may deviate from elastic behavior under small loads.
  • Continuum elasticity assumptions may fail at small material scales.

Purpose of the Study:

  • To investigate the scale-dependent elasticity of granular and nanoscale materials.
  • To determine the conditions under which continuum elasticity is no longer valid.
  • To model and understand the emergence of force chains and stress distributions.

Main Methods:

  • Utilized 2D and 3D computational models with interparticle harmonic interactions.
  • Simulated material behavior across a range of scales, from small (below O(100) particle diameters) to large.
  • Analyzed force chains, force distributions, and stress distributions.

Main Results:

  • Departures from elasticity were observed at small scales, consistent with model predictions.
  • These elastic deviations vanished at larger scales, where continuum elasticity holds.
  • Models successfully reproduced experimental findings regarding force chains and stress distributions.
  • The influence of anisotropy, disorder, and boundary conditions on material behavior was explored.

Conclusions:

  • Material scale is a critical factor in determining elastic behavior, particularly for granular and nanoscale systems.
  • Continuum elasticity is an approximation that breaks down below a characteristic scale.
  • The developed models provide a framework for understanding complex mechanical responses in discrete materials.