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Related Concept Videos

Three-Dimensional Analysis of Strain01:29

Three-Dimensional Analysis of Strain

Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
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...
Components of Stress01:23

Components of Stress

Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
Interestingly, the hidden cube faces also experience these stresses, equal and opposite to those on the...
Stress: General Loading Conditions01:15

Stress: General Loading Conditions

To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes.
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...
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.

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Related Experiment Video

Updated: Jun 25, 2026

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method
07:37

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method

Published on: January 16, 2019

Principal component analysis of shear strain effects.

Hao Chen1, Tomy Varghese

  • 1Department of Medical Physics, The University of Wisconsin-Madison, 1111 Highland Avenue, Madison, WI-53706, USA.

Ultrasonics
|February 10, 2009
PubMed
Summary

Lateral shear deformations create artifacts in strain imaging. Principal component analysis (PCA) strain images offer improved signal-to-noise and contrast-to-noise ratios compared to standard strain tensor images, enhancing diagnostic accuracy.

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Last Updated: Jun 25, 2026

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method
07:37

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method

Published on: January 16, 2019

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Published on: May 18, 2015

Area of Science:

  • Medical imaging
  • Biomedical engineering
  • Ultrasound elastography

Background:

  • Shear stresses are inherent in quasi-static strain imaging due to tissue slippage during axial deformation.
  • These shear stresses introduce artifacts, including rigid motion and deformation, into axial and lateral strain tensor images.
  • Understanding and mitigating these artifacts is crucial for accurate strain distribution depiction.

Purpose of the Study:

  • To evaluate the impact of lateral shear deformation artifacts on normal strain tensors.
  • To assess the effectiveness of principal component analysis (PCA) strain images in improving image quality.
  • To quantify shear strains using the lateral shear angle.

Main Methods:

  • Simulations and experimental validations were performed using uniformly elastic and single inclusion phantoms.
  • Lateral shear angles were varied during axial deformation to quantify shear strains.
  • Elastographic signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) were evaluated for varying axial (0-5%) and lateral (0-5 degrees) deformations.

Main Results:

  • PCA strain images (first and second principal components) demonstrated significantly higher SNRs (20 dB in simulations, 10 dB experimentally) and CNRs (at least 20 dB higher) compared to axial and lateral strain tensor images under lateral shear.
  • Lateral shear deformations degraded strain image quality, particularly at small axial deformations, though PCA provided a 1-2 dB improvement over axial strain tensor images.
  • Noise levels in axial and lateral strain tensor images increased substantially with larger axial deformations due to lateral shear.

Conclusions:

  • PCA strain images consistently provide superior elastographic SNR and CNR compared to axial strain tensor images in the presence of both axial and lateral shear deformations.
  • This improvement is validated through both simulation and experimental data.
  • PCA-based strain imaging offers a promising approach to mitigate artifacts and enhance diagnostic accuracy in ultrasound elastography.