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Related Concept Videos

Relation Between the Distributed Load and Shear01:23

Relation Between the Distributed Load and Shear

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Understanding the relationship between the distributed load and shear force in structural analysis is crucial for analyzing beams subjected to various loading conditions. Consider the case of a beam experiencing a distributed load, two concentrated loads, and a couple moment.
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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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Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Shearing Strain01:20

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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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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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A direct link between active matter and sheared granular systems.

Peter K Morse1, Sudeshna Roy2,3, Elisabeth Agoritsas4

  • 1Department of Chemistry, Duke University, Durham, NC 27710; peter.k.morse@gmail.com mmanning@syr.edu.

Proceedings of the National Academy of Sciences of the United States of America
|May 1, 2021
PubMed
Summary
This summary is machine-generated.

Researchers found that dense active matter and sheared amorphous solids share similar critical behaviors, like avalanche statistics. A new mean-field model accurately predicts this equivalence, offering a universal framework for disordered materials.

Keywords:
dense active matterdynamical mean-field theoryenergy landscapesgeneralized rheologysheared granular matter

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Area of Science:

  • Physics
  • Materials Science
  • Complex Systems

Background:

  • The mechanical properties of dense active matter and sheared amorphous solids exhibit striking similarities.
  • A rigorous understanding of the underlying mechanisms driving this observed equivalence is lacking.

Purpose of the Study:

  • To develop a theoretical model explaining the shared critical behavior of dense active matter and sheared amorphous solids.
  • To validate mean-field predictions in lower dimensions and identify unifying principles for disordered materials.

Main Methods:

  • Development of a mean-field model predicting critical behavior equivalence based on avalanche statistics.
  • Numerical simulations using an "athermal quasistatic random displacement" protocol in two dimensions.
  • Identification of a general class of perturbations bridging different force regimes.

Main Results:

  • The mean-field model accurately predicts equivalent critical behavior (avalanche statistics) in infinite dimensions, up to a rescaling factor.
  • These predictions show surprising accuracy in two-dimensional simulations, validating the model in low dimensions.
  • A perturbation framework was identified that smoothly connects localized forces in active matter to system-spanning displacements in sheared solids.

Conclusions:

  • Dense active matter and sheared amorphous solids share a universal framework governing their flow, deformation, and failure.
  • The developed mean-field model provides a powerful tool for predicting the behavior of diverse disordered materials.
  • This research bridges the gap between active and passive disordered systems, offering new insights into material mechanics.