Sensitivity analysis for parameter identification in quasi-static poroelasticity

This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and test...

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Vydané v:International journal for numerical and analytical methods in geomechanics Ročník 29; číslo 2; s. 163 - 185
Hlavní autori: Lecampion, Brice, Constantinescu, Andrei
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Chichester, UK John Wiley & Sons, Ltd 01.02.2005
Wiley
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ISSN:0363-9061, 1096-9853
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Abstract This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and tested on two numerical examples for the case of isotropic and homogeneous material. The presented formulations can be extended to more complex behaviour in poromechanics. Copyright © 2004 John Wiley & Sons, Ltd.
AbstractList This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi-static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and tested on two numerical examples for the case of isotropic and homogeneous material. The presented formulations can be extended to more complex behaviour in poromechanics.
This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and tested on two numerical examples for the case of isotropic and homogeneous material. The presented formulations can be extended to more complex behaviour in poromechanics. Copyright © 2004 John Wiley & Sons, Ltd.
Author Lecampion, Brice
Constantinescu, Andrei
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  givenname: Andrei
  surname: Constantinescu
  fullname: Constantinescu, Andrei
  email: andrei.constantinescu@lms.polytechnique.fr
  organization: Laboratoire de Mécanique des Solides, CNRS UMR7649, Ecole Polytechnique, 91128 Palaiseau Cedex, France
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Cites_doi 10.1080/01495738708927014
10.1080/174159794088027573
10.1002/nag.136
10.2514/3.10949
10.1016/S0021-9290(98)00161-4
10.1002/nme.1620200206
10.1063/1.1712886
10.1063/1.1721956
10.1016/0307-904X(87)90144-2
10.1016/0956-0521(91)90053-8
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Issue 2
Keywords Sensitivity analysis
Rock mechanics
Theoretical study
Soil mechanics
Inverse problem
Formulation
Poroelasticity
direct differentiation method
Example
inverse problems
Parameter
Numerical simulation
adjoint state method
Differentiation
parameter identification
poroelasticity
sensitivity analysis
Language English
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PublicationTitle International journal for numerical and analytical methods in geomechanics
PublicationTitleAlternate Int. J. Numer. Anal. Meth. Geomech
PublicationYear 2005
Publisher John Wiley & Sons, Ltd
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Cowin SC. Bone poroelasticity. Journal of Biomechanics 1999; 32:217-238.
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Mahnken R, Steinmann P. A finite element algorithm for parameter identification of material models for fluid saturated porous media. International Journal for Numerical and Analytical Methods in Geomechanics 2001; 25:415-434.
Tortorelli DA, Michaleris P. Design sensitivity analysis: overview and review. Inverse Problems in Engineering 1994; 1:71-103.
Zienkiewicz OC. The Finite Element Method. Mc-Graw Hill: New York, 1977.
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Cheng AHD, Predeleanu M. Transient boundary element formulation in poroelasticity. Applied Mathematical Modelling 1987; 11:285-290.
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1987; 11
1955; 26
1991; 2
1984; 20
1987; 10
1968; 17
2000
1941; 12
2004; 12
1987
1999; 32
2004
1982
1992
2003
2002
1994; 1
1993; 2
2001; 25
1968
1977
1992; 30
Nocedal (10.1002/nag.409-BIB24) 2002
Bonnet (10.1002/nag.409-BIB9) 1992
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Detournay (10.1002/nag.409-BIB5) 2004; 12
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Wang (10.1002/nag.409-BIB2) 2000
Predeleanu (10.1002/nag.409-BIB21) 1968; 17
Constantinescu (10.1002/nag.409-BIB6) 2004
Biot (10.1002/nag.409-BIB16) 1955; 26
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Vidal (10.1002/nag.409-BIB20) 1991; 2
Lecampion (10.1002/nag.409-BIB4) 2004
Mahnken (10.1002/nag.409-BIB8) 2001; 25
Curran (10.1002/nag.409-BIB14) 1987
Gill (10.1002/nag.409-BIB23) 1982
Cheng (10.1002/nag.409-BIB13) 1987; 11
Lions (10.1002/nag.409-BIB22) 1968
Zienkiewicz (10.1002/nag.409-BIB18) 1977
Coussy (10.1002/nag.409-BIB11) 2004
CEA (10.1002/nag.409-BIB17) 2003
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References_xml – reference: Lecampion B, Constantinescu A, Malinsky L. Identification of poroelastic constants of tight rocks from laboratory tests. International Journal of Geomechanics 2004, submitted.
– reference: Coussy O. Poromechanics. Wiley: New York, 2004.
– reference: Wang HF. Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology. Princeton University Press: Princeton, NJ, 2000.
– reference: Nocedal J, Wright SJ. Numerical Optimization. Springer: Berlin, 2002.
– reference: Cowin SC. Bone poroelasticity. Journal of Biomechanics 1999; 32:217-238.
– reference: Dems K, Mróz Z. Variational approach to sensitivity analysis in thermoelasticity. Journal of Thermal Stresses 1987; 10:283-306.
– reference: Mahnken R, Steinmann P. A finite element algorithm for parameter identification of material models for fluid saturated porous media. International Journal for Numerical and Analytical Methods in Geomechanics 2001; 25:415-434.
– reference: Cheng AHD, Ligget JA. Boundary integral equation method for linear poroelasticity with applications to soil consolidation. International Journal for Numerical Methods in Engineering 1984; 20:255-278.
– reference: Arora JS, Cardoso JB. Variational principle for shape sensitivity analysis. AIAA Journal 1992; 30:538-547.
– reference: Predeleanu M. Reciprocal theorem in the consolidation theory of porous media. Anal. Univ. Bucuresti, Seria Stiitele Naturii, Matematica, Mecanica 1968; 17:75-79.
– reference: Tortorelli DA, Michaleris P. Design sensitivity analysis: overview and review. Inverse Problems in Engineering 1994; 1:71-103.
– reference: Cheng AHD, Predeleanu M. Transient boundary element formulation in poroelasticity. Applied Mathematical Modelling 1987; 11:285-290.
– reference: Biot MA. Theory of elasticity and consolidation for a porous anisotropic solid. Journal of Applied Physics 1955; 26:182-185.
– reference: Gill PE, Murray W, Wright MH. Practical Optimization. Academic Press: New York, 1982.
– reference: Biot MA. General theory of three-dimensional consolidation. Journal of Applied Physics 1941; 12:155-164.
– reference: Zienkiewicz OC. The Finite Element Method. Mc-Graw Hill: New York, 1977.
– reference: Lions JL. Contrôle optimal des équations aux dérivées partielles. Dunod: Paris, 1968 (in French).
– reference: Vidal CA, Lee HS, Haber RB. The consistent tangent operator for design sensitivity analysis of history-dependent response. Computing Systems in Engineering 1991; 2(5/6):509-523.
– reference: Detournay E, Berchenko I. Thermoporoelastic experiments at url. International Journal of Rock Mechanics and Mining Sciences 2004; 12:155-164.
– year: 1982
– volume: 2
  start-page: 509
  issue: 5/6
  year: 1991
  end-page: 523
  article-title: The consistent tangent operator for design sensitivity analysis of history‐dependent response
  publication-title: Computing Systems in Engineering
– start-page: 73
  year: 1987
  end-page: 78
– volume: 17
  start-page: 75
  year: 1968
  end-page: 79
  article-title: Reciprocal theorem in the consolidation theory of porous media
  publication-title: Anal. Univ. Bucuresti, Seria Stiitele Naturii, Matematica, Mecanica
– volume: 12
  start-page: 155
  year: 2004
  end-page: 164
  article-title: Thermoporoelastic experiments at url
  publication-title: International Journal of Rock Mechanics and Mining Sciences
– volume: 2
  year: 1993
– year: 1968
– year: 2004
  article-title: Identification of poroelastic constants of tight rocks from laboratory tests
  publication-title: International Journal of Geomechanics
– year: 2002
– volume: 1
  start-page: 71
  year: 1994
  end-page: 103
  article-title: Design sensitivity analysis: overview and review
  publication-title: Inverse Problems in Engineering
– volume: 20
  start-page: 255
  year: 1984
  end-page: 278
  article-title: Boundary integral equation method for linear poroelasticity with applications to soil consolidation
  publication-title: International Journal for Numerical Methods in Engineering
– volume: 11
  start-page: 285
  year: 1987
  end-page: 290
  article-title: Transient boundary element formulation in poroelasticity
  publication-title: Applied Mathematical Modelling
– volume: 26
  start-page: 182
  year: 1955
  end-page: 185
  article-title: Theory of elasticity and consolidation for a porous anisotropic solid
  publication-title: Journal of Applied Physics
– volume: 30
  start-page: 538
  year: 1992
  end-page: 547
  article-title: Variational principle for shape sensitivity analysis
  publication-title: AIAA Journal
– year: 2004
– volume: 25
  start-page: 415
  year: 2001
  end-page: 434
  article-title: A finite element algorithm for parameter identification of material models for fluid saturated porous media
  publication-title: International Journal for Numerical and Analytical Methods in Geomechanics
– year: 2003
– year: 2000
– year: 1977
– year: 1992
– volume: 10
  start-page: 283
  year: 1987
  end-page: 306
  article-title: Variational approach to sensitivity analysis in thermoelasticity
  publication-title: Journal of Thermal Stresses
– volume: 32
  start-page: 217
  year: 1999
  end-page: 238
  article-title: Bone poroelasticity
  publication-title: Journal of Biomechanics
– volume: 12
  start-page: 155
  year: 1941
  end-page: 164
  article-title: General theory of three‐dimensional consolidation
  publication-title: Journal of Applied Physics
– volume: 10
  start-page: 283
  year: 1987
  ident: 10.1002/nag.409-BIB10
  publication-title: Journal of Thermal Stresses
  doi: 10.1080/01495738708927014
– volume: 2
  volume-title: Fundamentals of Poroelasticity, Comprehensive Rocks Engineering
  year: 1993
  ident: 10.1002/nag.409-BIB1
– volume: 12
  start-page: 155
  year: 2004
  ident: 10.1002/nag.409-BIB5
  publication-title: International Journal of Rock Mechanics and Mining Sciences
– volume: 1
  start-page: 71
  year: 1994
  ident: 10.1002/nag.409-BIB7
  publication-title: Inverse Problems in Engineering
  doi: 10.1080/174159794088027573
– volume: 25
  start-page: 415
  year: 2001
  ident: 10.1002/nag.409-BIB8
  publication-title: International Journal for Numerical and Analytical Methods in Geomechanics
  doi: 10.1002/nag.136
– volume: 30
  start-page: 538
  year: 1992
  ident: 10.1002/nag.409-BIB19
  publication-title: AIAA Journal
  doi: 10.2514/3.10949
– year: 2003
  ident: 10.1002/nag.409-BIB17
– year: 2002
  ident: 10.1002/nag.409-BIB25
– volume-title: Practical Optimization
  year: 1982
  ident: 10.1002/nag.409-BIB23
– volume-title: Poromechanics
  year: 2004
  ident: 10.1002/nag.409-BIB11
– volume: 32
  start-page: 217
  year: 1999
  ident: 10.1002/nag.409-BIB3
  publication-title: Journal of Biomechanics
  doi: 10.1016/S0021-9290(98)00161-4
– year: 2004
  ident: 10.1002/nag.409-BIB4
  publication-title: International Journal of Geomechanics
– volume-title: A Global Computational Approach in Engineering Problems: Identification and Fatigue
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  doi: 10.1063/1.1712886
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Snippet This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the...
This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi-static linear poroelasticity. We derive the...
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StartPage 163
SubjectTerms adjoint state method
Applied sciences
Buildings. Public works
Computation methods. Tables. Charts
direct differentiation method
Engineering Sciences
Exact sciences and technology
Geophysics
Geotechnics
inverse problems
Mechanics
parameter identification
Physics
poroelasticity
sensitivity analysis
Soil mechanics. Rocks mechanics
Solid mechanics
Structural analysis. Stresses
Title Sensitivity analysis for parameter identification in quasi-static poroelasticity
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https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fnag.409
https://www.proquest.com/docview/29630666
https://hal.science/hal-00111439
Volume 29
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