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Related Concept Videos

Normal Stress01:19

Normal Stress

1.5K
Normal stress is a type of stress that occurs when forces act perpendicular, or normal, to a material's cross-sectional area. This stress often arises in structures when subjected to axial loading, which is the application of force along the axis of an object. A practical example of this can be found in bridge truss members.
When a rod is under axial loading, the internal forces and corresponding stress are normal to the plane of the section, so it is termed normal stress. It's important to...
1.5K
Stress: General Loading Conditions01:15

Stress: General Loading Conditions

743
To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes....
743
True Stress and True Strain01:28

True Stress and True Strain

1.1K
Engineering stress is calculated as the load divided by the original, undeformed cross-sectional area. It approximates a material under load. This approximation is especially relevant post-yield in ductile materials. Though engineering stress-strain diagrams are often used for their convenience and accessibility, they can sometimes fall short in accuracy, particularly when dealing with large strain values.
In contrast, true stress offers a more precise portrayal. It is computed by dividing the...
1.1K
Stress Concentrations01:24

Stress Concentrations

834
Stress concentration is when stress intensifies near discontinuities such as holes or abrupt cross-sectional changes in a structural member. This localized stress can often surpass the average stress within the member. The stress distribution in flat bars, either with a circular hole or varying widths connected by fillets, can be determined experimentally using a photoelastic method. The results are based on ratios of geometric parameters like the ratio of the hole's radius to the smaller...
834
Stress Concentrations01:13

Stress Concentrations

813
The concept of stress concentration is crucial for understanding how materials respond under bending stresses, particularly when there are irregularities or discontinuities in the material's geometry. Normally, stress in a symmetric member subjected to pure bending is assumed to be uniformly distributed across the entire cross-section. However, this assumption does not hold when there are variations in the cross-sectional geometry or the presence of notches and holes.
The stress...
813
Measurements of Strain01:27

Measurements of Strain

2.8K
Strain quantifies the deformation of a material under force, typically measured as normal strain, which represents the change in length when compared with the original length. Electrical strain gauges are used for enhanced accuracy. These devices consist of a conductive wire mounted on a paper backing that adheres to the material's surface. These gauges operate on the piezoresistive effect, where the wire's electrical resistance changes in response to mechanical deformation. The strain...
2.8K

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Related Experiment Video

Updated: May 3, 2026

Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction
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Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction

Published on: May 20, 2018

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How Scale Breaks "Normalized Stress" and KL Divergence: Rethinking Quality Metrics.

Kiran Smelser, Kaviru Gunaratne, Jacob Miller

    IEEE Transactions on Visualization and Computer Graphics
    |January 26, 2026
    PubMed
    Summary
    This summary is machine-generated.

    Researchers developed a scale-invariant technique to improve accuracy metrics for high-dimensional data visualization. This addresses limitations in normalized stress and Kullback-Leibler divergence, enhancing dimension reduction evaluations.

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    Area of Science:

    • Data visualization
    • Machine learning
    • Computational biology
    • Social sciences

    Background:

    • High-dimensional data visualization relies on 2D scatter plots.
    • Quality metrics like normalized stress and Kullback-Leibler (KL) divergence assess projection accuracy.
    • Current metrics are sensitive to uniform scaling, impacting evaluation reliability.

    Purpose of the Study:

    • To investigate the impact of uniform scaling on normalized stress and KL divergence.
    • To develop a scale-invariant method for improving these dimension reduction quality metrics.
    • To validate the proposed technique using analytical and empirical methods.

    Main Methods:

    • Analytical investigation of scaling effects on stress and KL divergence.
    • Empirical evaluation of metric behavior under uniform scaling.
    • Development and application of a novel scale-invariant adjustment technique.

    Main Results:

    • Demonstrated significant sensitivity of normalized stress and KL divergence to uniform scaling.
    • Quantified the extent to which scaling affects metric values and dimension reduction evaluations.
    • Showcased the effectiveness of the proposed scale-invariant technique on a benchmark dataset.

    Conclusions:

    • Uniform scaling poses a challenge for accurate interpretation of dimension reduction quality metrics.
    • The introduced scale-invariant technique offers a reliable solution for evaluating projection faithfulness.
    • This advancement improves the assessment of complex, high-dimensional data visualization techniques.