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Elastic Strain Energy for Shearing Stresses

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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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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...

Shearing Stress

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Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
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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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Related Experiment Video

Updated: May 14, 2026

Measuring Material Microstructure Under Flow Using 1-2 Plane Flow-Small Angle Neutron Scattering

Measuring Material Microstructure Under Flow Using 1-2 Plane Flow-Small Angle Neutron Scattering

Published on: February 6, 2014

Fluid depletion in shear bands.

Roman Mani¹, Dirk Kadau, Dani Or

¹Computational Physics, IfB, ETH-Hönggerberg, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland. manir@ethz.ch

Physical Review Letters

|February 2, 2013

Summary

This summary is machine-generated.

In wet granular materials, pore liquid depletes in shear bands, contrary to expectations. This occurs due to liquid bridge rupture and reconfiguration, leading to a modified diffusion model for liquid migration.

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Measuring Material Microstructure Under Flow Using 1-2 Plane Flow-Small Angle Neutron Scattering

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The Assembly and Application of 'Shear Rings': A Novel Endothelial Model for Orbital, Unidirectional and Periodic Fluid Flow and Shear Stress

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Studying Large Amplitude Oscillatory Shear Response of Soft Materials

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Published on: April 25, 2019

Area of Science:

Geophysics
Soft Matter Physics
Fluid Dynamics

Background:

Granular materials exhibit complex behaviors when saturated with liquid.
Understanding liquid transport within shear bands is crucial for predicting material failure.
Conventional models suggest liquid influx into dilating zones.

Purpose of the Study:

To investigate the reconfiguration of pore liquid within shear bands in wet granular media.
To resolve the paradox of liquid depletion in dilatant shear bands.
To develop a microscale model for liquid transport at low saturation.

Main Methods:

Development of a microscale model for liquid transport.
Analysis of liquid bridge rupture and reconfiguration dynamics.
Measurement of liquid content profiles.
Comparison with numerical simulations.

Main Results:

Observed depletion of liquid in shear bands, contradicting conventional predictions.
Demonstrated that increased porosity due to dilatancy does not lead to liquid influx.
Validated microscale model predictions with experimental measurements.
Identified rupture and reconfiguration of liquid bridges as the primary mechanism.

Conclusions:

The study resolves the paradox of liquid depletion in shear bands.
A novel microscale model explains liquid transport driven by liquid bridge dynamics.
A modified diffusion description for rupture-induced liquid migration is proposed.