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Related Concept Videos

Shearing Strain01:20

Shearing Strain

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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...
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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

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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.
669
Elastic Strain Energy for Shearing Stresses01:20

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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Problem Solving on Stress and Strain01:22

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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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Circular Shaft - Stresses in Linear Range01:13

Circular Shaft - Stresses in Linear Range

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Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.
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Strain and Elastic Modulus01:15

Strain and Elastic Modulus

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The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear...
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Measurement of Compressive Stress-Strain Response at Small-Strains
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Shear modulus reconstruction by ultrasonically measured strain ratio.

Chikayoshi Sumi1, Hidenori Matsuzawa2

  • 1Department of Electrical and Electronics Engineering, Faculty of Science and Technology, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo, 102-8554, Japan. c-sumi@sophia.ac.jp.

Journal of Medical Ultrasonics (2001)
|June 10, 2016
PubMed
Summary

This study introduces new methods for stable shear modulus reconstruction in breast tissues. Method 3 offers faster reconstruction, especially for challenging tissues like scirrhous carcinoma.

Keywords:
human breast scirrhous carcinomaone-dimensional shear modulus reconstructionstabilizationstrain ratioultrasound

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Area of Science:

  • Medical imaging
  • Biomedical engineering
  • Elasticity imaging

Background:

  • Shear modulus reconstruction is crucial for diagnosing tissue abnormalities.
  • Existing one-dimensional (1D) methods face challenges with accuracy and stability, particularly in heterogeneous tissues.

Purpose of the Study:

  • To describe three previously developed 1D shear modulus reconstruction methods.
  • To introduce two new methods for stabilizing these 1D methods.
  • To evaluate the effectiveness and limitations of these methods for in vivo breast tissue analysis.

Main Methods:

  • Developed and compared three 1D shear modulus reconstruction methods using strain ratio.
  • Introduced regularization techniques (Methods 2 and 3) to stabilize reconstruction, especially in regions with high shear moduli.
  • Investigated low-pass filtering of strain ratio or inverse shear modulus, and low-resolution evaluation of reference strains to address reconstruction instability.

Main Results:

  • Method 1 is effective with high strain distribution accuracy.
  • Methods 2 and 3 provide stable reconstruction for heterogeneous tissues like scirrhous carcinoma.
  • Low-pass filtering of the strain ratio yielded more accurate inhomogeneity values than low-resolution reference strain evaluation, despite potential lateral instability.

Conclusions:

  • All presented methods enable real-time shear modulus reconstruction.
  • Method selection should be based on strain measurement accuracy and artifact occurrence for optimal application in ultrasonic imaging.