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Related Concept Videos

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...
Shearing Strain01:20

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...
Circular Shaft - Stresses in Linear Range01:13

Circular Shaft - Stresses in Linear Range

Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.
Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
Second Law of Thermodynamics00:53

Second Law of Thermodynamics

The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the chemical energy...

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Measuring Material Microstructure Under Flow Using 1-2 Plane Flow-Small Angle Neutron Scattering
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Nonequilibrium thermodynamics in sheared hard-sphere materials.

Charles K C Lieou1, J S Langer

  • 1Department of Physics, University of California, Santa Barbara, California 93106, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

This study merges amorphous plasticity theory with granular material physics to model shear flow in hard spheres. The research introduces compactivity as a key disorder metric, predicting strain rates near jamming transitions.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Amorphous plasticity is often described by shear-transformation-zone (STZ) theory.
  • Granular materials exhibit complex flow behavior governed by statistical mechanics.
  • Disordered systems, like granular materials and glasses, share thermodynamic similarities.

Purpose of the Study:

  • To develop a unified framework combining STZ theory and granular statistical mechanics.
  • To describe shear flow in disordered systems of thermalized hard spheres.
  • To introduce and utilize 'compactivity' as a measure of disorder.

Main Methods:

  • Developed equations of motion within a statistical thermodynamic framework.
  • Adapted concepts from molecular glass analysis to hard sphere systems.
  • Introduced compactivity (X = ∂V/∂S) as an analogue to effective temperature.

Main Results:

  • Derived STZ equations of motion for granular materials.
  • Predicted strain rate as a function of shear stress to pressure ratio.
  • Identified a dimensionless, temperature-like variable near jamming transitions.

Conclusions:

  • The unified theory provides insights into granular material flow.
  • The study offers a new perspective on the relationship between jamming and glass transitions.
  • Interpreted numerical simulations to validate theoretical predictions and understand internal rate factors.