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Related Concept Videos

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...
Dynamic Modulus of Elasticity of Concrete01:16

Dynamic Modulus of Elasticity of Concrete

The dynamic modulus of elasticity assesses how a concrete structure deforms under impact or dynamic loads. It is typically higher than the static modulus of elasticity, measured under slow, steady loading conditions.
The sonic test is a common method to determine the dynamic modulus. In this test, a concrete beam, sized either 6 x 6 x 30 inches or 4 x 4 x 20 inches, is clamped at its center. Vibrations are initiated at one end of the beam by an electromagnetic exciter unit powered by a...
Strain and Elastic Modulus01:15

Strain and Elastic Modulus

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...
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.
Shearing Stress01:18

Shearing Stress

Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
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...

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Related Experiment Video

Updated: Jun 12, 2026

Measurement of Compressive Stress-Strain Response at Small-Strains
02:58

Measurement of Compressive Stress-Strain Response at Small-Strains

Published on: December 5, 2025

Shear modulus estimation with vibrating needle stimulation.

Marko Orescanin1, Michael Insana

  • 1Department of Electrical and Computer Engineering and the Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign, Urbana, IL, USA. moresca2@illinois.edu

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
|June 10, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces an ultrasonic shear wave imaging method to measure the complex shear modulus of soft tissues. The technique accurately estimates elastic and viscous properties using two rheological models.

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Area of Science:

  • Biophysics
  • Biomaterials Science
  • Medical Imaging

Background:

  • Estimating the complex shear modulus of biphasic hydropolymers and soft biological tissues is crucial for understanding their mechanical properties.
  • Current methods may have limitations in accuracy or applicability to dynamic tissue behavior.

Purpose of the Study:

  • To develop and validate an ultrasonic shear wave imaging technique for precise complex shear modulus estimation.
  • To compare the performance of the Zener and Kelvin-Voigt rheological models in characterizing hydropolymers.

Main Methods:

  • Generating harmonic shear waves using an in-axis vibrated needle.
  • Synchronously tracking particle motion with Doppler pulses to estimate shear wave speed.
  • Employing a k-lag phase estimator for improved velocity estimation.
  • Fitting shear wave speed data to dispersion relation curves from rheological models.

Main Results:

  • The ultrasonic technique successfully estimated shear wave propagation speed.
  • Both the Zener and Kelvin-Voigt models yielded comparable complex shear modulus estimates.
  • The results demonstrated good agreement with independent shear rheometer measurements.

Conclusions:

  • Ultrasonic shear wave imaging provides a viable method for characterizing the viscoelastic properties of soft tissues and hydropolymers.
  • The developed technique and rheological modeling approach offer accurate estimations of elastic and viscous moduli.