43 research outputs found
Stabilizing Heteroscedastic Noise With the Generalized Anscombe Transform. Application to Accurate Prediction of the Resolution in Displacement and Strain Maps Obtained With the Grid Method.
International audienceThe objective of this paper is to show that it is possible to predict the noise level in displacement and strain maps obtained with the grid method, but that actual noise of camera sensors being heteroscedastic, it is necessary to stabilize this noise in grid images prior to employing the predicting formulas. The procedure used for this purpose relies on the Generalized Anscombe Transform. This transform is first described. It is then shown that experimental and theoretical resolutions in strain maps obtained with the grid method are in good agreement when this transform is employed
The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation
In linear anisotropic elasticity, the elastic properties of a medium are
described by the fourth rank elasticity tensor C. The decomposition of C into a
partially symmetric tensor M and a partially antisymmetric tensors N is often
used in the literature. An alternative, less well-known decomposition, into the
completely symmetric part S of C plus the reminder A, turns out to be
irreducible under the 3-dimensional general linear group. We show that the
SA-decomposition is unique, irreducible, and preserves the symmetries of the
elasticity tensor. The MN-decomposition fails to have these desirable
properties and is such inferior from a physical point of view. Various
applications of the SA-decomposition are discussed: the Cauchy relations
(vanishing of A), the non-existence of elastic null Lagrangians, the
decomposition of the elastic energy and of the acoustic wave propagation. The
acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The
Cauchy part governs the longitudinal wave propagation. We provide explicit
examples of the effectiveness of the SA-decomposition. A complete class of
anisotropic media is proposed that allows pure polarizations in arbitrary
directions, similarly as in an isotropic medium.Comment: 1 figur
Assessment of digital image correlation measurement errors: methodology and results
Optical full-field measurement methods such as Digital Image Correlation (DIC) are increasingly used in the field of experimental mechanics, but they still suffer from a lack of information about their metrological performances. To assess the performance of DIC techniques and give some practical rules for users, a collaborative work has been carried out by the Workgroup “Metrology” of the French CNRS research network 2519 “MCIMS (Mesures de Champs et Identification en Mécanique des Solides / Full-field measurement and identification in solid mechanics, http://www.ifma.fr/lami/gdr2519)”. A methodology is proposed to assess the metrological performances of the image processing algorithms that constitute their main component, the knowledge of which being required for a global assessment of the whole measurement system. The study is based on displacement error assessment from synthetic speckle images. Series of synthetic reference and deformed images with random patterns have been generated, assuming a sinusoidal displacement field with various frequencies and amplitudes. Displacements are evaluated by several DIC packages based on various formulations and used in the French community. Evaluated displacements are compared with the exact imposed values and errors are statistically analyzed. Results show general trends rather independent of the implementations but strongly correlated with the assumptions of the underlying algorithms. Various error regimes are identified, for which the dependence of the uncertainty with the parameters of the algorithms, such as subset size, gray level interpolation or shape functions, is discussed
The Virtual Fields Method for Extracting Constitutive Parameters From Full-Field Measurements: a Review
The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry
The closest tensors of higher symmetry classes are derived in explicit form
for a given elasticity tensor of arbitrary symmetry. The mathematical problem
is to minimize the elastic length or distance between the given tensor and the
closest elasticity tensor of the specified symmetry. Solutions are presented
for three distance functions, with particular attention to the Riemannian and
log-Euclidean distances. These yield solutions that are invariant under
inversion, i.e., the same whether elastic stiffness or compliance are
considered. The Frobenius distance function, which corresponds to common
notions of Euclidean length, is not invariant although it is simple to apply
using projection operators. A complete description of the Euclidean projection
method is presented. The three metrics are considered at a level of detail far
greater than heretofore, as we develop the general framework to best fit a
given set of moduli onto higher elastic symmetries. The procedures for finding
the closest elasticity tensor are illustrated by application to a set of 21
moduli with no underlying symmetry.Comment: 48 pages, 1 figur
Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts: reply to comment
Whole-field assessment of the effects of boundary conditions on the strain field in off-axis tensile testing of unidirectional composites
The objective of this paper is to present an experimental assessment of the effects of boundary conditions on the strain field in 10° off-axis tensile tests on unidirectional carbon/epoxy composites. It is shown experimentally by using a whole-field phase stepped grid technique that oblique tabbing of off-axis coupons results in a homogeneous strain field over the whole specimen, thus preventing premature failure near the tabs. A numerical sensitivity study reveals that the oblique angle is not very sensitive to the elastic moduli values. Therefore only estimates of the moduli are needed to derive the oblique angle. It is also shown by finite-element analysis that a 3° error on the oblique angle is acceptable in terms of stress concentrations near the tabs, but that a 7° error leads to significant stress concentrations for this material.<br/
Response to the discussion of the paper “Novel procedure for complete in-plane composite characterization using a single T-shaped specimen”
Noise in phase shifting interferometry
We present a theoretical analysis to estimate the amount of phase noise due to noisy interferograms in Phase Shifting Interferometry (PSI). We also analyze the fact that linear filtering transforms corrupting multiplicative noise in Electronic Speckle Pattern Interferometry (ESPI) into fringes corrupted by additive gaussian noise. This fact allow us to obtain a formula to estimate the standard deviation of the noisy demodulated phase as a function of the spectral response of the preprocessing spatial filtering combined with the PSI algorithm used. This phase noise power formula is the main result of this contribution