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Elastic Strain Energy for Shearing Stresses

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...

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Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
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Measurements of Strain

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Strain and Elastic Modulus

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Related Experiment Video

Updated: Jun 10, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Novel spline-based approach for robust strain estimation in elastography.

S Kaisar Alam¹

¹Riverside Research Institute, 156 William Street, New York, NY 10038, USA. kalam@rri-usa.org

Ultrasonic Imaging

|August 7, 2010

Summary

A new smoothing-spline strain estimator improves elastography by enhancing signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) without sacrificing resolution. This method refines strain estimation quality for clearer medical imaging.

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Last Updated: Jun 10, 2026

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Published on: April 16, 2017

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Area of Science:

Medical Imaging
Biomedical Engineering
Signal Processing

Background:

Robust strain estimation is crucial for medical elastography.
Current methods often trade resolution for improved signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR).

Purpose of the Study:

To develop a novel strain estimator that achieves high SNR and CNR without compromising resolution.
To enhance the quality of elastograms through improved strain estimation.

Main Methods:

A least-squares-based smoothing-spline strain estimator was proposed.
The method de-emphasizes displacements with lower correlation during strain computation.

Main Results:

The proposed estimator produced elastograms with high SNR and CNR.
Resolution was maintained without significant degradation.
Validation was performed using finite-element simulations and phantom experimental data.

Conclusions:

The smoothing-spline strain estimator offers a viable solution for high-quality elastography.
This technique enables improved diagnostic accuracy by preserving resolution while enhancing image quality.