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Publié par | Thesee |
Nombre de lectures | 31 |
Langue | English |
Poids de l'ouvrage | 7 Mo |
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N° d’ordre: 106
ECOLE CENTRALE DE LILLE
THESE
présentée en vue
d’obtenir le grade de
DOCTEUR
en
Spécialité: Micro et Nano Technologies, Acoustique et Télécommunications
par
YiFeng LI
DOCTORAT DELIVRE PAR L’ECOLE CENTRALE DE LILLE
Titre de la Thèse:
Développement d’outils de simulation numérique pour l’élastodynamique non
linéaire: Application à l’imagerie acoustique de défauts à l’aide de transducteur à
cavité chaotique.
Soutenue le 9 juillet devant le jury d’examen:
Président François Coulouvrat, DR, Institut Jean le Rond d'Alembert – UMR 7190
Jean Pierre Remenieras, IR HDR, Inserm U930 - CNRS FRE 2448 Rapporteur
Rapporteur Koen Van Den Abeele, PR, K.U. leuven Campus Kortrijk
Membre Philippe Pernod, PR, Ecole Centrale de Lille
Membre Vladimir Preobrazensky, PR, Ecole Centrale de Lille
Olivier Bou Matar – Lacaze, PR, Ecole Centrale de Lille Directeur de thèse
Thèse préparée dans le Laboratoire IEMN
Ecole Doctorale SPI 072 (Lille I, Lille III, Artois, ULCO, UVHC, EC Lille)
tel-00578755, version 1 - 22 Mar 2011
tel-00578755, version 1 - 22 Mar 2011CONTENTS
CONTENTS
CONTENTS...................................................................................................................................I
RESUME...................................................................................................................................... 1
INTRODUCTION ........................................................................................................................ 16
CHAPTER 1: INTRODUCTION TO NONLINEAR NONDESTRUCTIVE TESTING AND IMAGING... 21
1.1 Introduction............................................................................................................................... 21
1.2 Nonlinear Nondestructive Testing and Imaging Methods..................................................... 21
1.2.1 NEWS Methods ................................................................................................................................ 21
1.2.2 Linear and Nonlinear Ultrasonic Imaging Methods for NDT ...................................................... 22
1.2.3 TR and NEWS Combined Methods................................................................................................ 23
1.3 Nonlinear Elasticity and Elastodynamic Equations............................................................... 28
1.3.1 Nonlinear 1D Propagation Model in Heterogeneous Elastic Media............................................. 28
1.3.2 “Classical” and “Non-classical” Nonlinear Elasticity.................................................................... 29
1.3.3 Nonlinear Elastodynamic System of Equations ............................................................................. 40
1.4 Numerical Simulation Methods ............................................................................................... 44
1.4.1 Finite Difference Method ................................................................................................................. 45
1.4.2 Finite Volume Method...................................................................................................................... 46
1.4.3 Finite Element Method..................................................................................................................... 48
1.4.4 Pseudo-Spectral Method .................................................................................................................. 50
1.4.5 Discontinuous Galerkin Finite Element Method ........................................................................... 51
1.5 Pseudo-Spectral Simulation of 1D Nonlinear Propagation in Elastic Media ...................... 54
1.5.1 The Elastic Wave Solver .................................................................................................................. 54
1.5.2 Shock Wave Simulation ................................................................................................................... 57
1.5.3 Rod Resonance Simulation .............................................................................................................. 60
1.6 Conclusion.................................................................................................................................. 62
CHAPTER 2: THE NODAL DISCONTINUOUS GALERKIN METHOD .......................................... 64
2.1 Introduction............................................................................................................................... 64
2.2 Discontinuous Galerkin Finite Element Method Scheme in 2D............................................ 66
2.2.1 General Formulation of Discontinuous Galerkin Schemes........................................................... 66
2.2.2 Defining Discontinuous Galerkin Operators on Triangular Elements ........................................ 68
2.2.3 Numerical Fluxes in the Discontinuous Galerkin Method ............................................................ 72
2.2.4 Discontinuous Galerkin Operators on Quadrilateral Element..................................................... 74
2.2.5 Time-Stepping and Discrete Stability ............................................................................................. 76
2.3 Boundary Conditions................................................................................................................ 78
2.3.1 Open Boundaries .............................................................................................................................. 78
2.3.2 Stress Free and Fixed Surface Boundaries..................................................................................... 78
2.4 Sources ....................................................................................................................................... 80
I
tel-00578755, version 1 - 22 Mar 2011CONTENTS
2.5 Numerical Validation: Comparison with Analytical Solutions............................................. 81
2.5.1 Linear Isotropic Simulation of Lamb’s Problem........................................................................... 82
2.5.2 Linear Simulation of Elastic Waves Propagation in Anisotropic Apatite Material.................... 85
2.5.3 Attenuation........................................................................................................................................ 87
2.5.4 Simulation of Wave Propagation in “Classical” Nonlinear Elastodynamic Material ................ 90
2.6 Conclusion.................................................................................................................................. 96
CHAPTER 3: PML ABSORBING BOUNDARY CONDITION........................................................ 97
3.1 Introduction............................................................................................................................... 97
3.2 C-PML for Second-Order Elastodynamic Wave Equations ................................................. 98
3.2.1 Wave Equations for Anisotropic Solid in 2D ................................................................................. 98
3.2.2 C-PML Elastic Wave Equations in Frequency Domain................................................................ 99
3.2.3 Interpretation of C-PML as an Anisotropic Solid Medium........................................................ 100
3.2.4 C-PML Elastic Wave Equations in Time Domain ....................................................................... 101
3.2.5 Numerical Simulations ................................................................................................................... 103
3.3 C-PML Formulation for Piezoelectric Solid......................................................................... 111
3.3.1 Wave Equations for Piezoelectric Solid in 2D.............................................................................. 112
3.3.2 Formulation of C-PML in Frequency Domain ............................................................................ 112
3.3.3 Formulation of C-PML in Time Domain...................................................................................... 114
3.3.4 Numerical Simulations ................................................................................................................... 117
3.4 Nearly Perfectly Matched Layer (NPML) for Elastic Solid................................................ 121
3.4.1 Formulation of NPML for Elastic Wave Propagation ................................................................ 121
3.4.2 Comparison of NPML with C-PML.............................................................................................. 123
3.5 Stabilized Absorbing Boundary Layer.................................................................................. 129
3.5.1 Formulation of Stabilized Absorbing Boundary Layer............................................................... 129
3.5.2 Stability Analysis ............................................................................................................................ 131
3.5.3 Numerical Simulations of MPML for Anisotropic Solid Medium ..............