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Related Concept Videos

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...
Mohr's Circle for Plane Strain01:18

Mohr's Circle for Plane Strain

Mohr's circle is a crucial graphical method used to analyze plane strain by plotting strain on a set of cartesian coordinates, where the abscissa is normal strain ∈ and the ordinate is shear strain γ. Similarly to Mohr’s circle for plane stress, two points X and Y are plotted. Their coordinates are (∈x, -γXY) and (∈Y, γXY), respectively.
Mohr's circle visually represents the strain states under various conditions, which is essential for understanding material behavior. The center of Mohr's...
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...
Measurements of Strain01:27

Measurements of Strain

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 gauge...
Three-Dimensional Analysis of Strain01:29

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...
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.

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Related Experiment Video

Updated: Jun 12, 2026

Micro/Nano-scale Strain Distribution Measurement from Sampling Moiré Fringes
06:56

Micro/Nano-scale Strain Distribution Measurement from Sampling Moiré Fringes

Published on: May 23, 2017

Shearing interferometry and the moire method for shear strain determination.

K Patorski

    Applied Optics
    |June 12, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces two novel methods for calculating cross derivatives of in-plane displacements using lateral shear interferometry. These techniques enable precise optical measurements for advanced material analysis.

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    Area of Science:

    • Optical Metrology
    • Interferometry
    • Materials Science

    Background:

    • Accurate measurement of in-plane displacement derivatives is crucial for understanding material behavior under stress.
    • Existing methods for calculating cross derivatives can be complex and limited in application.

    Purpose of the Study:

    • To present novel methods for generating cross derivatives of in-plane displacements.
    • To demonstrate two distinct approaches for achieving this measurement using lateral shear interferometry.

    Main Methods:

    • Spatial filtering of composed diffraction structures.
    • Moire superimposition of conjugate-type lateral shear interferograms.

    Main Results:

    • Successful generation of cross derivatives of in-plane displacements was demonstrated.
    • Both presented methods proved effective in experimental validation.

    Conclusions:

    • The presented methods offer effective means for determining cross derivatives of in-plane displacements.
    • These techniques advance the capabilities of lateral shear interferometry for optical metrology.