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Related Concept Videos

Transformation of Plane Strain01:12

Transformation of Plane Strain

When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
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...
Transformation of Plane Stress01:18

Transformation of Plane Stress

Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's faces...
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
Problem Solving on Stress and Strain01:22

Problem Solving on Stress and Strain

Stress is a quantity that describes the magnitude of a force that causes deformation, generally defined as internal force per unit area. When forces pull on an object and cause its elongation, like the stretching of an elastic band, it is called tensile stress. When forces cause the compression of an object, it is known as compressive stress. When an object is being squeezed uniformly from all sides, like a submarine in the depths of the ocean, we call this kind of stress bulk stress (or volume...

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Related Experiment Video

Updated: Jul 7, 2026

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
09:00

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

Strain localization in a shear transformation zone model for amorphous solids.

M L Manning1, J S Langer, J M Carlson

  • 1Department of Physics, University of California, Santa Barbara, California 93106, USA. mmanning@physics.ucsb.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
PubMed
Summary
This summary is machine-generated.

This study models sheared disordered solids using shear transformation zones (STZs). The model accurately predicts strain localization and identifies a criterion for shear band formation based on initial conditions and nonlinear dissipation.

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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Related Experiment Videos

Last Updated: Jul 7, 2026

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
09:00

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

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Mechanics

Background:

  • Disordered solids exhibit complex mechanical behaviors, including strain localization.
  • Understanding shear band formation is crucial for predicting material failure.
  • Previous models often lack a comprehensive approach to transient dynamics and nonlinear effects.

Purpose of the Study:

  • To develop and validate a continuum model for sheared disordered solids using shear transformation zone (STZ) theory.
  • To investigate the mechanisms driving strain localization and shear band formation.
  • To derive a predictive criterion for shear banding based on initial material conditions.

Main Methods:

  • Mean-field continuum modeling based on shear transformation zone (STZ) theory.
  • Comparison of model predictions with existing simulation data (Shi, 2007).
  • Analysis of transient dynamics, effective temperature instabilities, and nonlinear energy dissipation.

Main Results:

  • The STZ model successfully reproduces simulation data and captures key features of strain localization.
  • An instability in transient dynamics can lead to perturbation growth, but does not guarantee shear band formation.
  • Nonlinear energy dissipation and perturbation growth interact to determine localization, leading to a derived criterion for shear banding.
  • Shear band width is determined by a dynamical scale dependent on strain rate, not a diffusion length.

Conclusions:

  • The STZ theory provides a robust framework for modeling strain localization in disordered solids.
  • Shear band formation is a complex process influenced by both inherent instabilities and nonlinear dissipation.
  • A predictive criterion based on initial conditions and material dynamics can determine the onset of shear banding.