Related Experiment Video
Updated: Jun 16, 2026
06:56
Micro/Nano-scale Strain Distribution Measurement from Sampling Moiré Fringes
Published on: May 23, 2017
Holographic strain analysis: extension of fringe-vector method to include perspective
Applied Optics
|February 19, 2010
Summary
This study extends a fringe analysis method to determine object deformation, even with varying illumination and observation angles. The new technique accounts for translations and geometric variations, improving strain and rotation tensor calculations.
Area of Science:
- Optical Metrology
- Solid Mechanics
- Experimental Mechanics
Background:
- Surface fringe analysis enables strain and rotation tensor determination for deformed objects.
- Previous methods required constant illumination and observation directions, limiting applicability.
Purpose of the Study:
- To extend existing fringe analysis theory to accommodate varying illumination and observation perspectives.
- To develop a method for calculating deformation tensors with non-constant optical geometries.
Main Methods:
- Theoretical extension of fringe vector analysis to include variable illumination and observation directions.
- Mathematical formulation of how bulk translations and linear geometric variations influence fringe vectors.
- Demonstration of calculability of linear variations from illumination and observation geometry.
Main Results:
- Fringe vectors are shown to be a sum of contributions from homogeneous transformations and geometric variations.
- Bulk translations and linear variations in illumination/observation directions are quantifiable.
- The extended theory successfully incorporates variable optical geometries.
Conclusions:
- The enhanced method allows for accurate determination of strain and rotation tensors under more general illumination and observation conditions.
- This advancement broadens the applicability of surface fringe analysis in experimental mechanics.
- The study provides a framework for analyzing deformations with complex optical setups.
Related Concept Videos
01:29Three-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...
01:12Transformation 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...
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
01:18Mohr'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...
Mohr's circle visually represents the strain states under various conditions, which is essential for understanding material behavior. The center of Mohr's...
01:14Bending of Curved Members - Strain Analysis
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.
The important part of bending analysis for such a member is the...
The important part of bending analysis for such a member is the...
01:22Generalized Hooke's Law
The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
01:27Measurements 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...