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Proceedings ArticleDOI

Performance Analysis and Experimental Validation of the Direct Strain Imaging Method

TL;DR: In this paper, an evaluation of the method's performance with respect to its operating parameter space is presented along with a preliminary validation based on actual experiments on composite material specimens under tension.
Abstract: Direct Strain Imaging accomplishes full field measurement of the strain tensor on the surface of a deforming body, by utilizing arbitrarily oriented engineering strain measurements originating from digital imaging. In this paper an evaluation of the method’s performance with respect to its operating parameter space is presented along with a preliminary validation based on actual experiments on composite material specimens under tension. It has been shown that the method exhibits excellent accuracy characteristics and outperforms methods based on displacement differentiation.Copyright © 2013 by ASME

Summary (2 min read)

2 Introduction

  • Classical methods for experimental full field measurements [1–15] rely on accomplishing strain measurements by differentiation of the full field of displacement.
  • It was made evident at the same time that the new approach was also more accurate than traditional approaches.
  • This paper aims at both presenting an analysis of the accuracy of DSI as it relates to the parameters that affect its performance, and at presenting its validation based on comparing its measurements with strain gauge data collected from actual experiments.
  • Approved for public release; distribution is unlimited.
  • The results of the parametric analysis are presented next, together with a discussion on the evaluation of the DSI performance.

3 Brief description of the DSI method

  • The typical experimental procedure for measuring the full field of deformation quantities according to the DSI method can be outlined as follows.
  • If the experiment is to take into consideration out of plane motion, two or more cameras are used so that the deformation is stereoscopically reconstructed.
  • This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
  • Given those engineering strains and the coordinates of the nodes, DSI can be used to calculate the strain tensor at any point w in the domain.
  • The terms rT (xi,x j) are vector integrals [16] and can be derived from the terms of Table 1.

4 Synthetic experiment design

  • In order to obtain metric characteristics of the response of DSI relative to the parameters controlling it, various parametric studies were designed and performed on synthetic experiments.
  • Approved for public release; distribution is unlimited.
  • To study the effects of the dot distribution, the synthetic experiment data included varying the mean dot distribution from 10 to 80 pixels with a step of 10.
  • The DSI procedure was applied on the un-deformed and deformed nodes and the error metrics where calculated for each value of the DOS.

4.1 Orthotropic plate with open hole

  • It is also included here for completeness.
  • The applied load forms an angle β with the major orthotropic axis as shown in Fig.
  • In the mathematical theory of elasticity it has been shown [27] that the composition of the force equilibrium differential equations along with the constitutive Eqns. (13) for the general case of multiply connected plane problems, can be reduced to a set of algebraic equations in terms of holomorphic functions expressed in the complex plane.
  • Additional modifications have been introduced [29] to account for rotations of the medium at infinity.
  • This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

4.2 Numerical Experiments

  • The synthetic experiments were performed by implementing the DSI algorithmics in Matlab [30] on an a second generation Intel i7 four core processor (2960XM).
  • The time required for the strain tensor evaluation per load increment as expressed by Eqns. (1) was found to be of order 10−3 seconds.
  • In Fig. 7 the same data is plotted for the case the noise level was 1/128 pixels.
  • The mean absolute error is around 30 µStrain for the point set of the entire field for most grid densities, while for the point set around the boundary is at the level of 100 µStrain This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

5 EXPERIMENTAL VALIDATION

  • The synthetic experiments provide the context for the verification (analytical validity) of the DSI method and also provide the basis for a direct approach for quantifying the actual error.
  • The width of the specimen was 50mm, the free length (height between the grips) approximately 25mm and the thickness approximately 4.1mm.
  • This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
  • The DSI domain of support was chosen to be 104 pixels, while the the basis function chosen was constructed by 3 terms.

6 CONCLUSIONS

  • In this paper a parametric analysis study was conducted and utilized synthetic experiments in order to evaluate the performance of the Direct Strain Imaging (DSI) method for a variety of user chosen parameters.
  • This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
  • While absolute number comparison is tenuous for the reasons noted above, DSI matches exceptionally well with the strain gauge time history measurements.

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Citations
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Patent
02 Aug 2013
TL;DR: In this article, a method and system for measuring and determining the full-field spatial distributions of strain tensor field components in a two or three-dimensional space, as a consequence of deformation under generalized loading conditions, is presented.
Abstract: A method and system for measuring and determining the full-field spatial distributions of strain tensor field components in a two or three-dimensional space, as a consequence of deformation under generalized loading conditions. One or more digital cameras may be used to acquire successive images of a deforming body with optically distinctive features on its surface. A method for determining the location of characteristic points of the surface features and another one for tracking these points as deformation occurs. Elongations between neighboring points on the vicinity of a location of interest are computed. The elongation between points is calculated even though discontinuities may exist between them. Strain tensor fields are directly calculated as a tensor approximation from these elongations without determining or using the displacement vector distributions.

27 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a method that employs Non-Uniform Rational B-spline (NURBs) based surrogate modeling to generate a very efficient representation of the combined constitutive and structural model response required for inverse characterization.

18 citations

Proceedings ArticleDOI
02 Aug 2015
TL;DR: This paper addresses the particular need for high-speed or “real-time” characterization of realistic anisotropic material systems such as laminated composites by presenting an evolutionary adaptation of earlier work into computationally efficient material characterization using response-surface surrogate models.
Abstract: In this paper we address the particular need for high-speed or “real-time” characterization of realistic anisotropic material systems such as laminated composites. This is driven by the desire to dynamically alter the loading paths applied by a multiaxial robotic test frame during the testing of a specimen, so that strain states are developed in the specimen in a manner that activates the maximum excitation of the specimen’s constitutive properties. In order to achieve this goal, we present an evolutionary adaptation of earlier work into computationally efficient material characterization using response-surface surrogate models. This approach is enhanced by the adoption of highly-parallel General Purpose Graphics Processing (GPGPU) computing. We discuss the challenges of adapting the characterization problem for GPGPU computing, particularly in terms of parallelization, synchronization, and approximation. Two parallelized algorithms for characterization are developed, and the merits of each are discussed. We then demonstrate validation results on a simple linear-elastic material system, and present statistical data which demonstrate the robustness of the approach in the presence of experimental noise. We conclude with remarks regarding the performance of the GPGPU-enabled characterization algorithm, and its applicability to more complex material systems.Copyright © 2015 by ASME

1 citations

References
More filters
Book
01 Jan 2000
TL;DR: In this article, the authors provide comprehensive background material and explain how to apply the methods and implement the algorithms directly in a unified framework, including geometric principles and how to represent objects algebraically so they can be computed and applied.
Abstract: From the Publisher: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. The book covers the geometric principles and how to represent objects algebraically so they can be computed and applied. The authors provide comprehensive background material and explain how to apply the methods and implement the algorithms directly.

15,558 citations

01 Jan 2001
TL;DR: This book is referred to read because it is an inspiring book to give you more chance to get experiences and also thoughts and it will show the best book collections and completed collections.
Abstract: Downloading the book in this website lists can give you more advantages. It will show you the best book collections and completed collections. So many books can be found in this website. So, this is not only this multiple view geometry in computer vision. However, this book is referred to read because it is an inspiring book to give you more chance to get experiences and also thoughts. This is simple, read the soft file of the book and you get it.

14,282 citations

Journal ArticleDOI
Ted Belytschko1, Y. Krongauz1, D. Organ1, Mark Fleming1, Petr Krysl1 
TL;DR: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined and it is shown that the three methods are in most cases identical except for the important fact that partitions ofunity enable p-adaptivity to be achieved.

3,082 citations


"Performance Analysis and Experiment..." refers background or methods in this paper

  • ...Such a polynomial basis can be constructed by concatenation of the complete order terms using the Pascal triangle of monomials [24, 26]....

    [...]

  • ...where W (w− (xi +x j)/2) = Wi j ≥ 0 is a weight function that decreases with distance as introduced by [24, 26]....

    [...]

Book
29 Jul 2002
TL;DR: In this paper, Galerkin et al. defined mesh-free methods for shape function construction, including the use of mesh-less local Petrov-Galerkin methods.
Abstract: Preliminaries Physical Problems in Engineering Solid Mechanics: A Fundamental Engineering Problem Numerical Techniques: Practical Solution Tools Defining Meshfree Methods Need for Meshfree Methods The Ideas of Meshfree Methods Basic Techniques for Meshfree Methods Outline of the Book Some Notations and Default Conventions Remarks Meshfree Shape Function Construction Basic Issues for Shape Function Construction Smoothed Particle Hydrodynamics Approach Reproducing Kernel Particle Method Moving Least Squares Approximation Point Interpolation Method Radial PIM Radial PIM with Polynomial Reproduction Weighted Least Square (WLS) Approximation Polynomial PIM with Rotational Coordinate Transformation Comparison Study via Examples Compatibility Issues: An Analysis Other Methods Function Spaces for Meshfree Methods Function Spaces Useful Spaces in Weak Formulation G Spaces: Definition G1h Spaces: Basic Properties Error Estimation Concluding Remarks Strain Field Construction Why Construct Strain Field? Historical Notes How to Construct? Admissible Conditions for Constructed Strain Fields Strain Construction Techniques Concluding Remarks Weak and Weakened Weak Formulations Introduction to Strong and Weak Forms Weighted Residual Method A Weak Formulation: Galerkin A Weakened Weak Formulation: GS-Galerkin The Hu-Washizu Principle The Hellinger-Reissner Principle The Modified Hellinger-Reissner Principle Single-Field Hellinger-Reissner Principle The Principle of Minimum Complementary Energy The Principle of Minimum Potential Energy Hamilton's Principle Hamilton's Principle with Constraints Galerkin Weak Form Galerkin Weak Form with Constraints A Weakened Weak Formulation: SC-Galerkin Parameterized Mixed Weak Form Concluding Remarks Element Free Galerkin Method EFG Formulation with Lagrange Multipliers EFG with Penalty Method Summary Meshless Local Petrov-Galerkin Method MLPG Formulation MLPG for Dynamic Problems Concluding Remarks Point Interpolation Methods Node-Based Smoothed Point Interpolation Method (NS-PIM) NS-PIM Using Radial Basis Functions (NS-RPIM) Upper Bound Properties of NS-PIM and NS-RPIM Edge-Based Smoothed Point Interpolation Methods (ES-PIMs) A Combined ES/NS Point Interpolation Methods (ES/NS-PIM) Strain-Constructed Point Interpolation Method (SC-PIM) A Comparison Study Summary Meshfree Methods for Fluid Dynamics Problem Introduction Navier-Stokes Equations Smoothed Particle Hydrodynamics Method Gradient Smoothing Method (GSM) Adaptive Gradient Smoothing Method (A-GSM) A Discussion on GSM for Incompressible Flows Other Improvements on GSM Meshfree Methods for Beams PIM Shape Function for Thin Beams Strong Form Equations Weak Formulation: Galerkin Formulation A Weakened Weak Formulation: GS-Galerkin Three Models Formulation for NS-PIM for Thin Beams Formulation for Dynamic Problems Numerical Examples for Static Analysis Numerical Examples: Upper Bound Solution Numerical Examples for Free Vibration Analysis Concluding Remarks Meshfree Methods for Plates Mechanics for Plates EFG Method for Thin Plates EFG Method for Thin Composite Laminates EFG Method for Thick Plates ES-PIM for Plates Meshfree Methods for Shells EFG Method for Spatial Thin Shells EFG Method for Thick Shells ES-PIM for Thick Shells Summary Boundary Meshfree Methods RPIM Using Polynomial Basis RPIM Using Radial Function Basis Remarks Meshfree Methods Coupled with Other Methods Coupled EFG/BEM Coupled EFG and Hybrid BEM Remarks Meshfree Methods for Adaptive Analysis Triangular Mesh and Integration Cells Node Numbering: A Simple Approach Bucket Algorithm for Node Searching Relay Model for Domains with Irregular Boundaries Techniques for Adaptive Analysis Concluding Remarks MFree2D(c) Overview Techniques Used in MFree2D Preprocessing in MFree2D Postprocessing in MFree2D Index References appear at the end of each chapter.

1,768 citations


"Performance Analysis and Experiment..." refers background or methods in this paper

  • ...According to [26] a good value for Mesh-Free approximations is around 2....

    [...]

  • ...Such a polynomial basis can be constructed by concatenation of the complete order terms using the Pascal triangle of monomials [24, 26]....

    [...]

  • ...where W (w− (xi +x j)/2) = Wi j ≥ 0 is a weight function that decreases with distance as introduced by [24, 26]....

    [...]

Frequently Asked Questions (2)
Q1. What contributions have the authors mentioned in the paper "Performance analysis and experimental validation of the direct strain imaging method" ?

In this paper an evaluation of the method ’ s performance with respect to its operating parameter space is presented along with a preliminary validation based on actual experiments on composite material specimens under tension. 

Finally, both the observed computational efficiency and the high accuracy of the DSI method also justify the future development of a time-filtering algorithm that will make it possible to reduce the error even further.