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Related Concept Videos

Residual Stresses in Bending01:18

Residual Stresses in Bending

In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
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...
Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

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.
If...
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.
Elasticity in Concrete01:20

Elasticity in Concrete

Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear portion of...
Elastic Curve from the Load Distribution01:16

Elastic Curve from the Load Distribution

The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments. Initially, this...

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Applying Permanent, Robust Stenciled Patterns of Fine Particles to Elastomeric Surfaces
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Published on: July 8, 2025

Application of numerical methods to elasticity imaging.

Benjamin Castaneda1, Juvenal Ormachea, Paul Rodríguez

  • 1Laboratorio de Imágenes Médicas, Pontificia Universidad Católica del Pertú.

Molecular & Cellular Biomechanics : MCB
|September 10, 2013
PubMed
Summary
This summary is machine-generated.

Elasticity imaging maps tissue stiffness for disease diagnosis. This study introduces various elasticity imaging techniques and discusses the role of numerical methods in quantitative analysis.

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Applying Permanent, Robust Stenciled Patterns of Fine Particles to Elastomeric Surfaces
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Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
14:14

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

Published on: April 16, 2017

Area of Science:

  • Biomedical Engineering
  • Medical Imaging Physics
  • Computational Mechanics

Background:

  • Pathological tissues often exhibit increased stiffness compared to healthy tissues.
  • Elasticity imaging aims to map tissue viscoelastic properties for clinical applications.
  • Research in elasticity imaging is an interdisciplinary effort combining biomechanics, imaging, and physics.

Purpose of the Study:

  • To introduce various elasticity imaging modalities.
  • To explain the working principles of qualitative and quantitative elasticity imaging techniques.
  • To highlight the application of numerical methods in elasticity imaging.

Main Methods:

  • Review of qualitative modalities: sonoelasticity, strain elastography, acoustic radiation force impulse.
  • Explanation of quantitative modalities: Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging.
  • Discussion of numerical methods for solving forward and inverse problems in quantitative elasticity imaging.

Main Results:

  • Detailed explanation of diverse elasticity imaging techniques.
  • Identification of key areas where numerical methods are applied.
  • Demonstration of total variation and AM-FM techniques for elasticity estimation.

Conclusions:

  • Elasticity imaging offers valuable clinical insights into tissue properties.
  • Numerical methods are crucial for quantitative elasticity imaging.
  • The study provides a foundation for understanding and applying advanced elasticity imaging techniques.