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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...

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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 Strain

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...

Three-Dimensional Analysis of Strain

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...

Normal Strain under Axial Loading

Normal Strain under Axial Loading

Normal strain under axial loading is an important concept in the field of mechanics of materials. Axial loading implies the application of a force along the axis of a material, like a column or bar. This force can either compress or stretch the material. In the context of axial loading, normal strain is the deformation experienced by the material in the direction of the loading force. It's calculated as the change in length divided by the original length of the material. This unitless ratio...

Transformation of Plane Strain

Transformation of Plane Strain

When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...

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Related Experiment Video

Updated: Jul 19, 2026

Magnetic Resonance Elastography Methodology for the Evaluation of Tissue Engineered Construct Growth

Magnetic Resonance Elastography Methodology for the Evaluation of Tissue Engineered Construct Growth

Published on: February 9, 2012

Resolution of axial shear strain elastography.

Arun Thitaikumar¹, Raffaella Righetti, Thomas A Krouskop

¹Ultrasonics Laboratory, Department of Diagnostic and Interventional Imaging, The University of Texas Medical School, Houston, TX, USA.

Physics in Medicine and Biology

|October 5, 2006

Summary

This study investigates axial shear strain elastography resolution using simulations. Findings show ultrasound bandwidth and beamwidth primarily determine resolution, with pitch also playing a role.

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Area of Science:

Medical imaging
Biomedical engineering
Ultrasound technology

Background:

Axial shear strain elastography (ASE) maps local shear strain during quasi-static axial compression.
Accurate spatial resolution is crucial for effective lesion characterization using ASE.

Purpose of the Study:

To investigate the spatial resolution of axial shear strain elastography.
To evaluate the influence of ultrasound system and signal processing parameters on ASE resolution.

Main Methods:

Simulations were performed using a stiff cylindrical lesion in a softer background.
Resolution was defined by the smallest inclusion size detectable at the interface.
Measurements were taken from axial shear strain profiles at a 45-degree orientation to beam propagation.

Main Results:

Spatial resolution is primarily determined by ultrasound system bandwidth and beamwidth.
The upper resolution limit is constrained by beamwidth and correlation window length, inversely scaled with bandwidth.
Resolution is directly proportional to transducer pitch and minimally affected by axial window shift.

Conclusions:

Ultrasound bandwidth and beamwidth are key determinants of axial shear strain elastography resolution.
Optimizing these parameters, along with pitch, is essential for improving lesion detection and characterization.
Further research can refine ASE techniques for enhanced diagnostic accuracy.