Inverse problems in elasticity

Inverse Problems

Volumn 21, Issue 2, 2005, Pages

  Bonnet, Marc ^a   Constantinescu, Andrei ^a  

^a LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY ELEMENT METHOD; COMPUTATIONAL COMPLEXITY; CONTINUUM MECHANICS; CRACK INITIATION; ELASTIC MODULI; ELASTICITY; FINITE ELEMENT METHOD; INCLUSIONS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; PROBLEM SOLVING; SENSITIVITY ANALYSIS; TOPOLOGY;

ADJOINT SOLUTION METHODS; CRACK SHAPE PERTURBATIONS; INVERSION ALGORITHMS; MODEL PARAMETERS;

INVERSE PROBLEMS;

EID: 17444412719     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/21/2/R01     Document Type: Review

References (142)

1. Allix O, Feissel P and Thévenet P 2003 A new identification strategy for dynamic problems with uncertain measurements COMPLAS: Proc. 7th Int. Conf. Computational Plasticity
2. Alves C and Ammari H 2001 Boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium SIAM J. Appl. Math. 62 94-106
3. Alves C J S and Ha Duong T 1999 Inverse scattering for elastic plane cracks Inverse Problems 15 91-7
4. Ammari H and Kang H 2004 Reconstruction of Small Inhomogeneities from Boundary Measurements (Lecture Notes in Mathematics vol 1846) (Berlin: Springer)
5. Ammari H, Kang H, Nakamura G and Tanuma K 2002 Complete asymptotic expansions of solutions of the system of elastostatics in the presence of an inclusion of small diameter and detection of an inclusion J. Elast. 67 97-129
6. Andriambololona H 1990 Optimisation des essais et recalage de modèles structuraux PhD Thesis Université de Besançon, France
7. Andrieux S, Ben Abda A and Bui H D 1997 Sur l'identification de fissures planes via le concept d'écart à la réciprocité en élasticité C. R. Acad. Sci., Paris II 324 1431-8
8. Andrieux S, Ben Abda A and Bui H D 1999 Reciprocity principle and crack identification Inverse Problems 15 59-65
9. Ballard P and Constantinescu A 1994 On the inversion of subsurface residual stresses from surface stress measurements J. Mech. Phys. Solids 42 1767-88
10. Bannour T, Ben Abda A and Jaoua M 1997 A semi-explicit algorithm for the reconstruction of 3D planar cracks Inverse Problems 13 899-917
11. Barbone E and Gokhale N H 2004 Elastic modulus imaging: on the uniqueness and nonuniqueness of the elastography inverse problem in two dimensions Inverse Problems 20 203-96
12. Barcilon V 1976 Inverse problem for vibrating beam J. Appl. Math. Phys. 27 346-58
13. Barcilon V 1979 On the multiplicity of solutions of the inverse problem for a vibrating beam SIAM J. Appl. Math. 37 605-13
14. Barcilon V 1982 Inverse problem for the vibrating beam in the free-clamped configuration Phil. Trans. R. Soc. A 304 211-51
15. Ben Abda A, Ben Ameur H and Jaoua M 1999 Identification of 2D cracks by boundary elastic measurements Inverse Problems 15 67-77
16. Ben Abda A and Bui H D 2001 Reciprocity principle and crack identification in transient thermal problems J. Inv. Ill-Posed Problems 9 1-6
17. Ben Abdallah J 1995 Inversion gaussienne appliqué à la correction paramétrique de modèles structuraux PhD Thesis Ecole Polytechnique, Paris
18. Ben Ameur H, Burger M and Hackl B 2004 Level set methods for geometric inverse problems in elasticity Inverse Problems 20 673-96
19. Ben-Haïm Y 1993 Identification of certain polynomial nonlinear structures by adaptive selectively-sensitive excitation ASME J. Vib. Acoust. 115 246-55
20. Bergounioux M and Kunish K 2003 On the structure of Lagrange multipliers for state-constrained systems System Control Lett. 48 169-76
21. Berthaud Y, Calloch S, Cluzel C, Hild F and Périé J-N 2000 Experiment/computation interactions by using digital image correlation Interferometry in Speckle Light, Theory and Applications ed P Jacquot and J-M Foumier (Berlin: Springer) pp 59-66
22. Bonnet M 1995 BIE and material differentiation applied to the formulation of obstacle inverse problems Eng. Anal. Bound. Elem. 15 121-36
23. Bonnet M 1999 Boundary Integral Equations Methods for Solids and Fluids (New York: Wiley)
24. Bonnet M and Ben Abdallah J 1998 Nonlinear Gaussian inversion applied to structural parameter identification Inverse Problems in Engineering: Theory and Practice ed D Delaunay, Y Jarny and K Woodbury (New York: ASME) pp 213-20
25. Bonnet M, Burczyński T and Nowakowski M 2002 Sensitivity analysis for shape perturbation of cavity or internal crack using BIE and adjoint variable approach Int. J. Solids Struct. 39 2365-85
26. Bonnet M and Guzina B B 2004 Sounding of finite solid bodies by way of topological derivative Int. J. Numer. Methods Eng. 61 2344-73
27. Bonnet M and Reynier M 1998 On the estimation of the geometrical support of modelling defects using the distributed error in constitutive equation Inverse Problems, Control and Shape Optimization (Carthage, Tunisia) pp 65-70
28. Brenner S C and Ridgway Scott L 1994 The Mathematical Theory of Finite Element Methods (Berlin: Springer)
29. Bui H D 1995 Sur quelques problèmes inverses élastiques en mécanique de l'endommagement Deuxième Colloque National de Calcul des Structures (France: Hermès) pp 26-35
30. Bui H D and Constantinescu A 2000 Spatial localization of the error of constitutive law for the identification of defects in elastic bodies Arch. Mech. 52 511-22
31. Bui H D, Constantinescu A and Maigre H 1999 Diffraction acoustique inverse de fissure plane: solution explicite pour un solide borné C. R. Acad. Sci., Paris. II 327 971-6
32. Bui H D, Constantinescu A and Maigre H 2004 Numerical identification of linear cracks in 2D elastodynamics using the instantaneous reciprocity gap Inverse Problems 20 993-1001
33. Burczyński T, Bonnet M, Fedelinski P and Nowakowski M 2002 Sensitivity analysis and identification of material defects in dynamical systems Syst. Anal. Modelling Simul. 42 559-74
34. Burger M 2004 Levenberg-Marquardt level set methods for inverse obstacle problems Inverse Problems 20 259-82
35. Calderon A P 1980 On an inverse boundary value problem Seminar on Numerical Analysis and its applications to Continuum Physics (Rio de Janeiro: Soc. Brasilian de Matematica) pp 65-73
36. Cast3M 2003 A general purpose code for solving partial differential equations by the finite element method, developed by the French Atomic Energy Commission, http://www-cast3m.cea.fr
37. Charalambopoulos A and Dassios G 1992 Inverse scattering via low-frequency moments J. Math. Phys. 33 4206-16
38. Charalambopoulos A, Gintides D and Kiriaki K 2002 The linear sampling method for the transmission problem in three-dimensional linear elasticity Inverse Problems 12 547-58
39. Chavent G, Kunisch K and Roberts J E 1999 Primal-dual formulations for parameter estimation problems Computational and Applied Mathematics vol 18 ed M A Raupp, J Douglas Jr, J Koiller and G P Menzala pp 173-229
40. Chen G and Zhou J 1992 Boundary Element Methods (New York: Academic)
41. Chouaki A, Ladevèze P and Proslier L 1996 An updating of structural dynamic model with damping Inverse Problems in Engineering: Theory and Practice ed D Delaunay, M Raynaud and K Woodbury (New York: ASME) pp 335-42
42. Cimetière A, Delvare F, Jaoua F and Pons F 2001 Solution of the Cauchy problem using iterated Tikhonov regularization Inverse Problems 17 553-70
43. Claire D, Hild F and Roux S 2004 A finite element formulation to identify damage fields Int. J. Numer. Methods Eng. 61 189-208
44. Colton D, Haddar H and Piana M 2003 The linear sampling method in inverse electromagnetic scattering theory Inverse Problems 19 S105-S137
45. Colton D and Kirsch A 1996 A simple method for solving inverse scattering problems in the resonance region Inverse Problems 12 383-93
46. Colton D and Kress R 1992 Inverse Acoustic and Electromagnetic Scattering Theory (Berlin: Springer)
47. Constantinescu A 1994 Sur l'identification des modules élastiques PhD Thesis Ecole Polytechnique, France
48. Constantinescu A 1995 On the identification of elastic moduli from displacement-force boundary measurements Inverse Problems Eng. 1 293-315
49. Constantinescu A 1998 On the identification of elastic moduli in plates Inverse Problems in Engineering Mechanics ed G S Dulikravich and M Tanaka (Amsterdam: Elsevier) pp 205-14
50. Constantinescu A, Ivaldi D and Stolz C 2003 Identification du chargement thermique transitoire par controle optimal 6eme Colloque National de Calcul des Structures vol 1 ed M Potier-Ferry and M Bonnet and A Bignonnet (Palaiseau: Ecole Polytechnique) pp 185-92
51. Constantinescu A and Tardieu N 2001 On the identification of elastoviscoplastic constitutive laws from indentation tests Inverse Problems Eng. 9 19-44
52. Cowin S C and Mehrabadi M M 1990 Eigentensors of linear elastic materials Q. J. Mech. Appl. Math. 43 14
53. Dassios G 2000 Energy functionals in scattering theory and inversion of low frequency moments Wavefield Inversion ed A Wirgin (Berlin: Springer) pp 1-58
54. Dassios G and Kleinman R 2000 Low Frequency Scattering (Oxford: Oxford University Press)
55. Delattre B, Ivaldi D and Stolz C 2002 Application du contrôle optimal à l'identification d'un chargement thermique Rev. Eur. Elem. Finis 11 393-404
56. Dems K and Mróz Z 1986 On a class of conservation rules associated with sensitivity analysis in linear elasticity Int. J. Solids Struct. 22 737-58
57. Deraemaeker A, Ladevèze P and Leconte Ph 2002 Reduced bases for model updating in structural dynamics based on constitutive relation error Comput. Methods. Appl. Mech. Eng. 191 2427-44
58. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Dordrecht: Kluwer)
59. Eschenauer H A, Kobelev V V and Schumacher A 1994 Bubble method for topology and shape optimization of structures Struct. Optim. 8 42-51
60. Eskin G and Ralston J 1994 On the inverse boundary value for linear isotropic elasticity Inverse Problems 18 907-21
61. Feijóo G R, Oberai A and Pinsky P M 2004 An application of shape optimization in the solution of inverse acoustic scattering problems Inverse Problems 20 199-228
62. Feuardent V 1997 Amélioration des modèles par recalage: application aux structures spatiales PhD Thesis ENS Cachan, France
63. Flannery B P, Deckman H W, Roberge W G and D'Amico K L 1987 Three-dimensional microtomography Science 237 1439-44
64. Forestier R, Chastel Y and Massoni E 2003 3D inverse analysis model using semi-analytical differentiation for mechanical parameter identification Inverse Problems Eng. 11 255-71
65. Freund L B 1998 Dynamical Fracture Mechanics (Cambridge: Cambridge University Press)
66. Gallego R and Rus G 2004 Identification of cracks and cavities using the topological sensitivity boundary integral equation Comput. Mech. 33 154-63
67. Gao Z and Mura T 1989 On the inversion of residual stresses from surface measurements ASME J. Appl. Mech. 56508-13
68. Garreau S, Guillaume P and Masmoudi M 2001 The topological asymptotic for PDE systems: the elasticity case SIAM J. Control. Optim. 39 1756-78
69. Gavrus A, Massoni E and Chenot J L 1996 An inverse analysis using a finite element model for identification of Theological parameters Comput. Methods Appl. Mech. Eng. 60 447-54
70. Geymonat G and Pagano S 2003 Identification of mechanical properties by displacement field measurement: a variational approach Meccanica 38 535-45
71. Grédiac M and Pierron F 2004 Numerical issues in the virtual fields method Int. J. Numer. Methods Eng. 59 1287-312
72. Grédiac M, Toussaint E and Pierron F 2002 Special virtual fields for the direct determination of material parameters with the virtual fields method: 1. Principle and definition Int. J. Solids Struct. 39 2691-705
73. Grédiac M, Toussaint E and Pierron F 2002 Special virtual fields for the direct determination of material parameters with the virtual fields method: 2. Application to in-plane properties Int. J. Solids Struct. 39 2707-30
74. Gurtin M E 1972 The Linear Theory of Elasticity (Handbuch der Physik, vol Vla/2,) (Berlin: Springer)
75. Guzina B B and Bonnet M 2004 Small-obstacle asymptotics and scalar wave imaging in preparation
76. Guzina B B and Bonnet M 2004 Topological derivative for the inverse scattering of elastic waves Q. J. Mech. Appl. Math. 57 161-79
77. Guzina B B and Chikichev I 2004 From imaging to material identification: a generalized concept of topological sensitivity ECCOMAS 2004 Conf. (CD-ROM Proc.) ed P Neittanmäki et al (Barcelona: Int. Ass. Computational Mechanics)
78. Guzina B B, Nintcheu Fata S and Bonnet M 2003 On the stress-wave imaging of cavities in a semi-infinite solid Int. J. Solids Struct. 40 1505-23
79. Hansen P C 1998 Rank-Deficient and Discrete Ill-Posed Problems (Philadelphia, PA: SIAM)
80. Hugues T J R 1987 The Finite Element Method - Linear Static and Dynamic Finite Element Analysis (Englewood Cliffs, NJ: Prentice Hall)
81. Ikehata M 1990 Inversion formulas for the linearized problem for an inverse boundary value problem in elastic prospection SIAMJ. Appl. Math. 50 1635-44
82. Ikehata M 1993 An inverse problem for the plate in the Love-Kirchhoff theory SIAMJ. Appl. Math. 53 942-70
83. Ikehata M 1995 The linearization of the Dirichlet to Neumann map in anisotropic plate theory Inverse Problems 11 165-81
84. Isaacson D and Isaacson E L 1989 Comment on Calderon's paper: on an inverse boundary value problem Math. Comput. 52 553-9
85. Jackowska-Strumillo L, Sokolowski J and Zochowski A 2002 Topological optimization and inverse problems Comput. Assist. Mech. Eng. Sci. 10 163-76
86. Johnson K L 1985 Contact Mechanics (Cambridge: Cambridge University Press)
87. Kikuchi N and Oden J T 1988 Contact Problems in Elasticity: Study of Variational Inequalities and Finite Element Methods (Philadelphia, PA: SIAM)
88. Kirsch A 1993 The domain derivative and two applications in inverse scattering theory Inverse Problems 9 81-96
89. Kohn R and McKenney A 1990 Numerical implementation of a variational method for electric impedance tomography Inverse Problems 6 389-414
90. Kohn R and Vogelius M 1984 Determining conductivity by boundary measurements Commun. Pure Appl. Math. 37 289-98
91. Kohn R and Vogelius M 1985 Determining conductivity by boundary measurements: II. Interior results Commun. Pure Appl. Math. 38 643-67
92. Kohn R and Vogelius M 1987 Relaxation of a variational method for impedance computed tomography Commun. Pure Appl. Math. 40 745-77
93. Kohn R V and Löwe B D 1988 A variational method for parameter identification Math. Modelling Numer. Anal. 1 119-58
94. Koslov V A, Maz'ya V G and Fomin A F 1991 An iterative method for solving the Cauchy problem for elliptic equations Comput. Math. Phys. 3145-52
95. Kress R 1995 Integral equation methods in inverse obstacle scattering Eng. Anal. Bound. Elem. 15 171-80
96. Kress R 1996 Inverse elastic scattering from a crack Inverse Problems 12 667-84
97. Kupradze V D 1963 Dynamical Problems in Elasticity (Progress in Solids Mechanics vol 3) (Amsterdam: North-Holland)
98. Kurpinar E and Karchevsky A L 2004 Numerical solution of the inverse problem for the elasticity system for horizontally stratified media Inverse Problems 20 953-76
99. Ladevèze P 1999 Nonlinear Computational Structural Mechanics. New Approaches and Non-Incremental Methods of Calculation (Mechanical Engineering Series) (Berlin: Springer)
100. Ladevèze P and Chouaki A 1999 Application of a posteriori error estimation for structural model updating Inverse Problems 15 49-58
101. Ladevèze P and Leguillon D 1983 Error estimates procedures in the finite element method and applications SIAM J. Numer. Anal. 20 485-509
102. Ladevèze P, Reynier M and Nedjar D 1993 Parametric correction of finite element models using modal tests Inverse Problems in Engineering Mechanics ed H D Bui and M Tanaka (Berlin: Springer) pp 91-100
103. Langenberg K J, Brandfass M, Hannemann R, Kostka J, Marklein R, Mayer K and Pitsch A 2000 Inverse scattering with acoustic, electromagnetic, and elastic waves as applied in nondestructive evaluation Wavefield Inversion ed A Wirgin (Berlin: Springer) pp 59-118
104. Langenberg K J and Marklein R 2005 Transient elastic waves applied to nondestructive testing of transversely Isotropie lossless materials: a coordinate-free approach Wave Motion 41 247-61
105. Leonard K R, Malyarenko E V and Hinders M K 2002 Ultrasonic Lamb wave tomography Inverse Problem 18 1795-808
106. Lin C-L and Wang J-N 2003 Uniqueness in inverse problems for an elasticity system with residual stress by a single measurement Inverse Problems 19 807-20
107. Link M 1993 Requirements for the structure of analytical models used for parameter identification Inverse Problems in Engineering Mechanics ed H D Bui and M Tanaka (Berlin: Springer) pp 133-46
108. Mahnken R and Stein E 1996 Parameter identification for viscoplastic models based on analytical derivatives of a least-square functionals and stability investigations Int. J. Plast. 12 451-79
109. Maniatty A M and Zabaras N J 1994 Investigation of regularization parameters and error estimating in inverse elasticity problems Int. J. Numer. Methods Eng. 37 1039-52
110. Marin L and Lesnic D 2002 Boundary element solution for the Cauchy problem in linear elasticity using singular value decomposition Comput. Methods Appl. Mech. Eng. 191 3257-70
111. Marin L and Lesnic D 2003 BEM first-order regularisation method in linear elasticity for boundary identification Comput. Methods Appl. Mech. Eng. 192 2059-71
112. Marklein R, Mayer K, Hannemann R, Krylow T, Balasubramanian K, Langenberg K J and Schmitz V 2002 Linear and nonlinear inversion algorithms applied in nondestructive evaluation Inverse Problems 18 1733-59
113. Martin P A 2003 Acoustic scattering by inhomogeneous obstacles SIAM J. Appl. Math. 64 297-308
114. Menke W 1984 Geophysical Data Analysis: Discrete Inverse Theory (New York: Academic)
115. Mottershead J E and Friswell M I 1993 Model updating in structural dynamics: a review J. Sound Vib. 167 347-75
116. Nakamura G and Uhlmann G 1994 Global uniqueness for an inverse boundary problem arising in elasticity Invent. Math. 118 457-74
117. Nakamura G and Uhlmann G 2002 Global uniqueness for an inverse boundary value problem arising in elasticity Invent. Math. 152 205-7 (erratum)
118. Nintcheu Fata S and Guzina B B 2004 A linear sampling method for near-field inverse problems in elastodynamics Inverse Problems 20 713-36
119. Nintcheu Fata S, Guzina B B and Bonnet M 2003 A computational basis for elastodynamic cavity identification in a semi-infinite solid Comput. Mech. 32 370-80
120. Nishimura N and Kobayashi S 1995 Determination of cracks having arbitrary shape with boundary integral method Eng. Anal. Bound. Elem. 15 189-97
121. Oden J T and Reddy J N 1976 Variational Methods in Theoretical Mechanics (Berlin: Springer)
122. Petryk H and Mróz Z 1986 Time derivatives of integrals and functionals defined on varying volume and surface domains Arch. Mech. 38 694-724
123. Plessix R E, De Roeck Y H and Chavent G 1999 Waveform inversion of reflection seismic data for kinematic parameters by local optimization SIAM J. Sci. Comput. 20 1033-52
124. Ramananjaona C, Lambert M, Lesselier D and Zolésio J P 2001 Shape reconstruction of buried obstacles by controlled evolution of a level set: from a min-max formulation to numerical experimentation Inverse Problems 17 1087-111
125. Reddy J N 1993 Introduction to the Finite Element Method (New York: McGraw-Hill)
126. Reynier M 1990 Sur le contrôle de modélisations éléments finis: recalage à partir d'essais dynamiques PhD Thesis Université Pierre et Marie Curie, Paris, France
127. Robertson R L 1997 Boundary identifiability of residual stress via the Dirichlet to Neumann map Inverse Problems 13 1107-19
128. Rus G, Bonnet M and Gallego R 2004 Crack shape sensitivity by the adjoint variable method using a boundary-only integral, in preparation
129. SalenÇon J 2001 Handbook of Continuum Mechanics (General Concepts, Thermoelasticity) (Berlin: Springer)
130. Santos J E 2002 On the solution of an inverse scattering problem in seismic while-drilling technology Comput. Methods Appl. Mech. Eng. 191 2403-25
131. Schmerr L W, Song S J and Sedov A 2002 Ultrasonic flaw sizing inverse problems Inverse Problems 18 1775-93
132. Schumacher A 1995 Topologieoptimierung von Bauteilstrukturen unter Verwendung von Lochpositionierungskriterien PhD Thesis University of Siegen, Germany
133. Sokolowski J and Zochowski A 1999 On the topological derivative in shape optimization SIAM J. Control Optim. 37 1251-72
134. Sokolowski J and Zolesio J P 1992 Introduction to Shape Optimization. Shape Sensitivity Analysis (Springer Series in Computational Mathematics vol 16) (Berlin: Springer)
135. Stavroulakis G and Antes H 1997 Nondestructive elastostatic identification of unilateral cracks through BEM and neural networks Comput. Mech. 20 439-51
136. Tarantula A 1987 Inverse Problem Theory (New York: Elsevier)
137. Tardieu N and Constantinescu A 2000 On the determination of elastic coefficients from indentation experiments Inverse Problems 16 577-88
138. Tikhonov A N and Arsenin V Y 1977 Solutions to Ill-Posed Problems (New York: Winston-Wiley)
139. Unger D J 2001 Analytical Fracture Mechanics (New York: Dover)
140. Weglein A B et al 2003 Inverse scattering series and seismic exploration Inverse Problems 19 R27-R83
141. Wexler A and Mandel C 1985 An impedance computed tomography algorithm and system for ground water and hazardous waste imaging Proc. 2nd Annual Canadian/American Conf. on Hydrogeology: Hazardous Wastes in Ground Water - A Soluble Dilemma (Banff, June) pp 156-61
142. Zimmermann D C and Kaouk M 1994 Structural damage detection using a minimum rank update theory ASME J. Vib. Acoust. 116 222-31