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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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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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The stress-strain relationship in ductile materials such as structural steel or aluminium is intricate and progresses through several stages. When a specimen is loaded, it initially exhibits a linear length increase, depicted by a steep straight line on the stress-strain diagram. It indicates the material is elastically deforming and will return to its original shape once unloaded. However, when a critical stress value is reached, plastic deformation begins. This stage sees substantial...
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Stress-Strain Diagram - Brittle Materials01:24

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Brittle materials, including glass, cast iron, and stone, exhibit unique characteristics. They fracture without considerable change in their elongation rate, indicating that their breaking and ultimate strength are equivalent. Such materials also show lower strain levels at the point of rupture. The failure in brittle materials predominantly results from normal stresses, as evidenced by the rupture created along a surface perpendicular to the applied load. These materials do not display...
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Most bones contain compact and spongy osseous tissue, but their distribution and concentration vary based on the bone's overall function.
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The compacting factor test is a method used to assess the workability of concrete. It is  especially suitable for concrete mixes containing aggregates up to one and a half inches in size. This test involves specialized equipment consisting of two truncated cone-shaped hoppers and a cylinder, all with polished interior surfaces to minimize friction.
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Strain localization in dry sheared granular materials: A compactivity-based approach.

Xiao Ma1, Ahmed Elbanna1

  • 1Department of Civil and Environmental Engineering, University of Illinois, Urbana-Champaign, Illinois, USA.

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|September 27, 2018
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Summary
This summary is machine-generated.

This study models strain localization in granular materials, finding that higher pressures lead to ductile fault zones, while lower pressures cause brittle behavior and strength drops. This impacts earthquake dynamics and fault structure.

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Area of Science:

  • Geophysics
  • Materials Science
  • Statistical Mechanics

Background:

  • Shear banding is prevalent in natural fault zones and laboratory granular material experiments.
  • Understanding strain localization dynamics is crucial for fault gouge strength, earthquake energy partitioning, and rheological transitions.

Purpose of the Study:

  • To develop a physics-based continuum model for strain localization in sheared granular materials.
  • To investigate shear band initiation and growth under various loading conditions.
  • To identify implications for strength evolution and the ductile-to-brittle transition.

Main Methods:

  • Utilized the shear transformation zone (STZ) theory, a nonequilibrium statistical thermodynamic framework, to describe grain-scale dynamics.
  • Employed a finite strain computational framework for numerical simulations.
  • Analyzed localization patterns under diverse loading conditions.

Main Results:

  • Numerical results mimic observed localization patterns in field and laboratory settings.
  • Shear zones exhibit more ductile responses under higher confining pressures, lower dilatancy, and looser initial conditions.
  • Lower pressures, higher dilatancy, and denser initial conditions promote brittle responses and significant strength drops.

Conclusions:

  • The model provides insights into strength evolution mechanisms in dry sheared granular materials.
  • Findings contribute to physics-based multiscale models of fault zone instabilities.
  • The study clarifies conditions favoring ductile versus brittle fault zone behavior.