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Related Concept Videos

Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

479
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...
479
Normal and Shear Force01:14

Normal and Shear Force

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When a beam is subjected to different loads, such as weight, pressure, or other external forces, internal forces are generated within the beam. These forces can have a significant impact on the overall stability and strength of the structure. Engineers use various methods to analyze and determine the magnitude and direction of these internal forces. One common technique used to determine internal forces in beams is the method of sections. This method involves considering an imaginary point or...
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Shearing Stress01:19

Shearing Stress

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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.
1.8K
Shear and Bending Moment Diagram: Problem Solving01:24

Shear and Bending Moment Diagram: Problem Solving

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When analyzing a beam supporting concentrated loads and a distributed load, drawing the shear and bending moment diagrams is essential. These diagrams help understand the internal forces and moments acting on the beam, which is crucial for designing safe and efficient structures. Follow these steps to create the shear and bending moment diagrams:
Draw a Free-Body Diagram: Start by drawing a free-body diagram of the entire beam, including the concentrated loads, distributed load, and reaction...
3.0K
Shearing Strain01:20

Shearing Strain

1.3K
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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Singularity Functions for Shear01:26

Singularity Functions for Shear

418
In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous  variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
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Related Experiment Video

Updated: Jan 14, 2026

Viscoelastic Characterization of Soft Tissue-Mimicking Gelatin Phantoms using Indentation and Magnetic Resonance Elastography
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SW-VEI-Net: A Physics-Informed Deep Neural Network for Shear Wave Viscoelasticity Imaging.

Haoming Lin, Zhongjun Ma, Yunxiang Wang

    IEEE Transactions on Bio-Medical Engineering
    |January 12, 2026
    PubMed
    Summary
    This summary is machine-generated.

    A new physics-informed neural network, SW-VEI-Net, accurately maps tissue viscoelasticity using shear wave elastography (SWE). This method improves liver fibrosis staging and lesion detection by precisely measuring elastic and viscous moduli.

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    Related Experiment Videos

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    Viscoelastic Characterization of Soft Tissue-Mimicking Gelatin Phantoms using Indentation and Magnetic Resonance Elastography
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    Area of Science:

    • Biomedical Engineering
    • Medical Imaging
    • Artificial Intelligence

    Background:

    • Quantitative viscoelasticity imaging using shear wave elastography (SWE) faces challenges due to complex wave physics and reconstruction method limitations.
    • Accurate assessment of both elastic and viscous moduli is crucial for diagnosing conditions like liver fibrosis.

    Purpose of the Study:

    • To develop and validate SW-VEI-Net, a physics-informed neural network (PINN) for simultaneous reconstruction of shear elastic and viscous moduli.
    • To enhance the accuracy, interpretability, and clinical applicability of SWE.

    Main Methods:

    • Developed SW-VEI-Net, a dual-network PINN integrating viscoelastic wave equations and a dual-loss function.
    • Validated the model on tissue-mimicking phantoms, a rat liver fibrosis model, and clinical data.
    • Compared SW-VEI-Net against state-of-the-art methods including SWENet and dispersion fitting (DF).

    Main Results:

    • SW-VEI-Net achieved higher accuracy in shear elastic modulus reconstruction compared to SWENet.
    • Viscoelastic parameter maps from SW-VEI-Net showed comparable results to DF with enhanced robustness.
    • SW-VEI-Net demonstrated superior performance in liver fibrosis staging (AUC 0.85 for ≥F2, 0.91 for =F4) compared to SWENet and DF.
    • Strong agreement was observed with a commercial ultrasound system in healthy volunteers.

    Conclusions:

    • SW-VEI-Net offers a significant advancement in SWE by accurately and simultaneously quantifying elastic and viscous moduli.
    • The method shows substantial clinical potential for early detection of hepatic fibrosis and malignant lesions.
    • Integrating deep learning with wave physics enhances SWE capabilities for precise viscoelastic biomarker mapping.