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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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Related Experiment Video

Updated: Jul 16, 2026

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

Published on: September 29, 2019

Critical packing in granular shear bands.

S Fazekas¹, J Török, J Kertész

¹Department of Theoretical Physics, Budapest University of Technology and Economics (BME), H-1111 Budapest, Hungary.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 16, 2007

Summary

This study simulates granular media deformation, revealing a critical packing density within shear bands. This critical state, driven by dilation-compaction balance, is key to understanding material failure and forms dynamic random loose packing.

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Last Updated: Jul 16, 2026

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

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$Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction$

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Published on: May 20, 2018

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Published on: February 6, 2014

Area of Science:

Geophysics
Materials Science
Computational Physics

Background:

Granular materials exhibit complex behaviors under stress.
Understanding strain localization is crucial for predicting material failure.

Purpose of the Study:

To simulate granular media deformation in a 3D setup.
To investigate the self-organization of strain localization and shear band formation.
To identify and characterize critical packing densities within shear bands.

Main Methods:

Realistic three-dimensional simulation of idealized granular media.
Axisymmetric triaxial shear test to induce slow deformation.
Analysis of spontaneous strain localization and shear band evolution.

Main Results:

Demonstrated the existence of a critical packing density within the shear band.
Showed that this critical density arises from a dynamic equilibrium of dilation and compaction.
Observed that the density outside the shear band retains initial packing memory.
Found critical density depends on friction, defining dynamic random loose packing at infinite friction.

Conclusions:

A critical packing density is a defining characteristic of shear bands in granular media.
The shear band reaches an asymptotic critical state independent of initial conditions.
Dynamic random loose packing represents a limit state for granular materials under shear.