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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

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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.
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The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
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Yield Criteria for Ductile Materials under Plane Stress01:25

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In designing structural elements and machine parts using ductile materials, it is crucial to ensure that these components withstand applied stresses without yielding. Yielding is initially determined through a tensile test, which evaluates the material's response to uniaxial stress. However, tensile stress is insufficient when components face biaxial or plane stress conditions This condition requires advanced criteria to predict failure.
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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...
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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...
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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.
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Fabry-Perot Cavity Optimization for Absolute Strain Sensing Using Finite Element Analysis.

João M B Pereira1,2, Paula M P Gouvea3, Arthur M B Braga3

  • 1Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, Gavea, Rio de Janeiro 22451-900, Brazil.

Sensors (Basel, Switzerland)
|November 14, 2023
PubMed
Summary
This summary is machine-generated.

A novel finite element method (FEM) model for Fabry-Perot Interferometers (FPI) accurately measures substrate strain. This optical sensor design eliminates the need for prior strain calibration, ensuring repeatable and precise measurements.

Keywords:
Fabry–Perot interferometerfinite element analysisin-fiber Fabry–Perotoptical fiber sensingstrain sensing

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Area of Science:

  • Optical Engineering
  • Materials Science
  • Mechanical Engineering

Background:

  • Fabry-Perot Interferometers (FPI) are optical sensors used for strain measurement.
  • Accurate strain measurement is crucial in various engineering applications.
  • Existing FPI sensors may require complex calibration procedures.

Purpose of the Study:

  • To develop and validate a finite element method (FEM) model for analyzing the optical-mechanical behavior of an FPI.
  • To investigate the strain measurement accuracy of FPI sensors.
  • To propose an improved FPI cavity geometry for accurate and repeatable strain measurement without calibration.

Main Methods:

  • Finite Element Method (FEM) modeling was employed to simulate the FPI's behavior.
  • The FEM model was validated against theoretical predictions and experimental data.
  • The model was used to analyze strain distribution within the FPI and host substrate.

Main Results:

  • The FEM model accurately predicted the FPI's optical-mechanical performance.
  • Simulations revealed that the measured strain often differs from the absolute substrate strain.
  • A novel cavity geometry was proposed, demonstrating repeatable fabrication and accurate strain measurement without calibration.

Conclusions:

  • The developed FEM model provides a reliable tool for FPI analysis.
  • Optimized FPI cavity design can achieve precise absolute strain measurement.
  • This advancement simplifies FPI sensor application and enhances measurement reliability.