Full-Field Measurements and Identification in Solid Mechanics

Full-Field Measurements and Identification in Solid Mechanics......Page 2
COPYRIGHT......Page 3
Table of Contents......Page 4
Foreword......Page 14
Introduction......Page 16
1.1. Introduction......Page 19
1.2.1. Absolute or differential measurement......Page 20
1.2.2. Main concepts......Page 22
1.3.1. Spatial frequency......Page 29
1.3.2. Spatial filtering......Page 34
1.4. Classification of optical measurement techniques......Page 36
1.4.1. White light measurement methods......Page 37
1.4.2. Interference methods......Page 39
1.4.4. Synthetic sensitivity vectors......Page 41
1.4.5. The different types of interferometric measurements......Page 42
1.4.6. Holography, digital holography......Page 45
1.4.7. Conclusion......Page 46
1.5. Bibliography......Page 47
2.1. Introduction......Page 48
2.2. Concept of light polarization......Page 49
2.3. Birefringence phenomenon......Page 50
2.4. The law of optico-mechanics......Page 51
2.5.1. Plane polariscope......Page 52
2.5.2. Circular polariscope......Page 55
2.5.4. Photoelastic coating......Page 57
2.6. Measurement of photoelastic constant C......Page 59
2.7.1. Using a plane polariscope......Page 60
2.7.2. Using a circular polariscope......Page 64
2.8.2. Particular points......Page 65
2.8.3. Stress separation and integration of the equilibrium equations......Page 66
2.9. Three-dimensional photoelasticity......Page 67
2.9.1. The method of stress freezing and mechanical slicing......Page 68
2.9.2. Optical slicing......Page 69
2.9.3. Application example......Page 73
2.11. Bibliography......Page 74
3.2. Principle......Page 77
3.3. Surface encoding......Page 79
3.4. Moiré......Page 80
3.5.1. Global extraction procedure......Page 82
3.5.2. Local phase detection: phase shifting......Page 83
3.5.3. Measuring both components of the displacement......Page 86
3.6. Sensitivity to out-of-plane displacements......Page 87
3.7. Grid defects......Page 88
3.8.1. Explicit method......Page 89
3.8.3. Large strain......Page 90
3.9. Fringe projection......Page 91
3.10. Deflectometry......Page 94
3.11.1. Off-axis tensile test of a unidirectional composite coupon......Page 97
3.11.2. Rigid body displacement......Page 99
3.11.3. SEM measurement......Page 100
3.11.4. Characterization of lens distortion......Page 101
3.12. Conclusion......Page 104
3.13. Bibliography......Page 105
4.1. Introduction......Page 108
4.2. Basics of wave optics......Page 109
4.2.1. Light diffraction......Page 110
4.2.2. Interference......Page 111
4.3.1. Recording the hologram......Page 112
4.3.2. Numerical reconstruction with the discrete Fresnel transform......Page 114
4.3.3. Numerical reconstruction using convolution with adjustable magnification......Page 115
4.3.4. Sensitivity vector......Page 116
4.4.1. Phase difference......Page 118
4.5.1. Principle......Page 119
4.5.3. Experimental set-up......Page 120
4.5.4. Application to synthetic concrete subjected to three-point bending......Page 122
4.6.1. Recording digital color holograms......Page 127
4.6.2. Application to composite material subjected to a short beam test......Page 128
4.7. Conclusion......Page 133
4.9. Bibliography......Page 134
5.1. Introduction......Page 140
5.2. What is speckle interferometry?......Page 141
5.2.1. Simplified principle ? correlation fringes......Page 143
5.2.2. Speckle field and specklegram statistics in a nutshell......Page 144
5.2.3. Speckle field transformation ? small perturbation theory......Page 146
5.2.4. Phase change?deformation law ? sensitivity vector......Page 147
5.2.5. Success or failure of experiments ? central role of decorrelation......Page 148
5.3. Optical point of view......Page 149
5.4.1. Measurement of the out-of-plane component......Page 151
5.4.2. Measurement of the in-plane component [LEE 70]......Page 152
5.4.3. 3C?3D: three components attached to three-dimensional objects......Page 153
5.4.4. Partial derivatives of the displacement ? shearography......Page 154
5.4.5. Shape measurement and other considerations......Page 155
5.5.1. One-image methods......Page 156
5.5.2. Phase-shifting methods......Page 157
5.5.3. Advanced methods......Page 158
5.5.4. Phase unwrapping......Page 159
5.6. Dynamic deformations and vibrations......Page 161
5.7. Setup calibration......Page 163
5.7.2. Determination of the sensitivity vector......Page 164
5.8. Specifications and limits......Page 165
5.9. Final remarks, outlook and trends......Page 166
5.10. Bibliography......Page 168
6.1. Background......Page 171
6.2.1. Images......Page 172
6.2.2. Texture of images......Page 173
6.2.3. Guiding principles......Page 175
6.2.4. Correlation coefficients......Page 177
6.2.5. Subpixel interpolation......Page 178
6.2.6. Local approaches......Page 180
6.2.7. Optimization algorithms......Page 182
6.2.8. Global approaches......Page 183
6.3.1. Main error sources......Page 186
6.3.2. Uncertainty and spatial resolution......Page 187
6.3.3. Noise sensitivity......Page 188
6.4. Stereo-correlation or 3D-DIC......Page 189
6.4.1. The stereovision technique......Page 190
6.4.2. 3D displacement measurement by stereo-correlation......Page 194
6.4.3. Computation of surface strains from 3D displacements......Page 195
6.5. Conclusions......Page 196
6.6. Bibliography......Page 197
7.2.1. Three related steps......Page 205
7.2.2. Framework for the differentiation of displacement measurements......Page 206
7.2.3. The main families of methods for differentiating data......Page 208
7.2.4. Quality of the reconstruction......Page 209
7.3.1. A simple one-dimensional example......Page 211
7.3.2. Finite differences......Page 212
7.3.3. Global least squares ? polynomial basis......Page 213
7.3.4. Filtering through a convolution kernel......Page 214
7.4.1. General presentation......Page 217
7.4.2. Global least squares ? Finite element basis......Page 218
7.4.3. Local least squares ? polynomial basis......Page 220
7.4.4. Three converging points of view......Page 221
7.5.1. Splitting the reconstruction error......Page 223
7.5.2. Estimation of approximation error......Page 224
7.5.3. Estimation of random error......Page 225
7.6.1. Constant signal-to-noise ratio......Page 228
7.6.2. A pragmatic criterion......Page 230
7.7. Taking the time dimension into consideration......Page 232
7.9. Bibliography......Page 234
8.2.1. Inversion......Page 236
8.2.2. Constitutive parameter identification......Page 243
8.3.1. Gradient-based methods......Page 245
8.3.2. Other methods......Page 249
8.4.1. Finite element model updating......Page 250
8.4.2. Constitutive relation error......Page 251
8.4.3. Methods based on equilibrium satisfaction......Page 252
8.4.4. Reciprocity gap......Page 254
8.6. Bibliography......Page 255
9.1. Introduction......Page 260
9.2.1. Principles of the method......Page 262
9.2.2. The “direct mechanical problem? and finite element analysis......Page 265
9.3.1. Theory......Page 267
9.3.2. Objective functions and minimization procedure......Page 269
9.3.3. Structural sensitivities......Page 275
9.4.1. Full-field measurements for the FEMU method......Page 277
9.4.2. Application to the material behavior......Page 278
9.4.3. Identification accuracy......Page 280
9.5. Conclusion......Page 281
9.6. Bibliography......Page 282
10.1. Introduction......Page 288
10.2. CEG in the linear elastic case: heterogeneous behavior and full-fieldmeasurement......Page 289
10.2.1. First variant: exact enforcement of kinematic measurements......Page 291
10.2.3. Comments......Page 296
10.2.4. Some numerical examples......Page 297
10.3.1. Formulation......Page 301
10.3.2. Numerical method......Page 303
10.4. Formulations based on the Legendre?Fenchel transform......Page 306
10.5. Suitable formulations for dynamics or vibration......Page 308
10.6. Conclusions......Page 310
10.7. Bibliography......Page 311
11.2. General principle......Page 314
11.3.2. Developing the PVW......Page 316
11.3.3. Special virtual fields......Page 318
11.3.4. Virtual fields optimized with respect to measurement noise......Page 320
11.3.5. Virtual fields defined by subdomains......Page 322
11.3.6. Examples......Page 324
11.3.7. Plate bending......Page 326
11.3.8. Large deformations: example of hyperelasticity......Page 332
11.4.2. Elastoplasticity......Page 334
11.4.3. Hyperelastic behavior......Page 337
11.5. Conclusion......Page 338
11.6. Bibliography......Page 339
12.1. Theoretical basis......Page 344
12.1.1. Homogeneous elastic medium......Page 345
12.1.3. Incremental formulation......Page 347
12.2. Finite difference implementation......Page 348
12.3. Finite element implementation......Page 350
12.4.1. Application to beam theory......Page 353
12.4.2. Loading identification......Page 355
12.4.3. Identification of a heterogeneous stiffness field......Page 356
12.5. Simultaneous identification of stiffness and loading fields......Page 358
12.6. Spectral sensitivity and reconditioning......Page 360
12.7. Damage......Page 362
12.8. Application to a biaxial test carried out on a composite material......Page 364
12.8.1. Damage modeling......Page 365
12.8.2. Adapted expression of the reconditioned equilibrium gap......Page 367
12.8.3. Application to a biaxial test......Page 368
12.9. Exploitation of measurement uncertainty......Page 371
12.10. Conclusions......Page 372
12.11. Bibliography......Page 373
13.1. Introduction......Page 376
13.2. The reciprocity gap method......Page 378
13.2.2. Fundamental property of the reciprocity gap......Page 380
13.3. Identification of cracks in electrostatics......Page 381
13.3.1. Identification formulas for the plane of the cracks......Page 383
13.3.2. Complete identification of cracks......Page 384
13.4. Crack identification in thermoelasticity using displacement measurements......Page 386
13.5. Conclusions and perspectives......Page 390
13.6. Bibliography......Page 391
14.1. Introduction......Page 392
14.2. Definitions and properties of the localized phenomena being considered......Page 393
14.3.1. Direct observation......Page 399
14.3.4. Digital image correlation......Page 400
14.3.6. X-ray tomography......Page 401
14.4.1. Emergence and development of shear bands in a sand specimen under planestrain revealed by stereophotogrammetry......Page 403
14.4.2. Comparison of stereophotogrammetry and digital image correlation for abiaxial test of a soft clay-rock specimen......Page 404
14.4.4. Characterization of severe discontinuities: stereophotogrammetry andcorrelation......Page 406
14.4.5. Localization on the grain scale: the contribution of discrete DVC......Page 407
14.4.7. Piobert?Lüders band in steel......Page 408
14.4.8. Portevin?Le Châtelier band......Page 409
14.5. The use of enriched kinematics......Page 410
14.5.1. Displacement discontinuity......Page 411
14.6. Localization of the discontinuity zone......Page 412
14.6.2. The use of correlation residuals......Page 413
14.7. Identification of fracture parameters......Page 414
14.8. Conclusion......Page 418
14.9. Bibliography......Page 419
15.2.1. How can we appreciate spatial heterogeneity?......Page 423
15.2.3. Inverse problem......Page 425
15.2.4. Statistical description/morphological model......Page 426
15.2.5. Coupling of identification with an exogenous field......Page 429
15.3. Examples of local field characterization......Page 430
15.3.1. EBSD analysis and orientation imaging microscopy......Page 431
15.4.1. Glass wool......Page 435
15.4.2. Identification......Page 438
15.5. Second example: crystal plasticity......Page 439
15.5.1. Multiscale approach for identification of material mechanical behavior......Page 440
15.5.2. Methodology......Page 442
15.5.3. Numerical simulation of mechanical behavior......Page 443
15.6. Conclusions......Page 446
15.7. Bibliography......Page 447
16.1. Introduction......Page 450
16.2.1. Constitutive equations......Page 452
16.2.2. Heat equation......Page 454
16.2.3. Energy balance over a load?unload cycle......Page 455
16.3. Metrological considerations......Page 457
16.3.1. Physics of radiation preliminaries......Page 458
16.3.2. Calibration......Page 459
16.3.3. Thermal noise and thermal drift......Page 463
16.4.1. Diffusion equation for thin plates......Page 465
16.4.2. Diffusion equation for straight beams......Page 466
16.4.3. Diffusion equation for a monotherm material volume element......Page 467
16.4.4. Integral transforms and quadrupole method related to thick media......Page 468
16.5. Concluding comments and prospects......Page 474
16.6. Bibliography......Page 475
List of Authors......Page 479
Index......Page 484