메뉴 건너뛰기




Volumn 60, Issue 5, 2012, Pages 857-881

Multiscale modeling of a fluid saturated medium with double porosity: Relevance to the compact bone

Author keywords

Biot model; Compact bone; Double porous medium; Fading memory; Homogenization

Indexed keywords

BIOT MODELS; COMPACT BONE; DOUBLE POROUS MEDIUM; FADING MEMORY; HOMOGENIZATION;

EID: 84857922539     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2012.01.013     Document Type: Article
Times cited : (72)

References (54)
  • 1
    • 0026627499 scopus 로고
    • Deformable porous media with double porosity. quasi-static. i: Coupling effects
    • J. Auriault, and C. Boutin Deformable porous media with double porosity. quasi-static. i: coupling effects Transp. Porous Media 7 1992 63 82
    • (1992) Transp. Porous Media , vol.7 , pp. 63-82
    • Auriault, J.1    Boutin, C.2
  • 2
    • 0027334616 scopus 로고
    • Deformable porous media with double porosity. Quasi-statics. II. Memory effects
    • J. Auriault, and C. Boutin Deformable porous media with double porosity. quasi-static. ii: memory effects Transp. Porous Media 10 1993 153 169 (Pubitemid 23389588)
    • (1993) Transport in Porous Media , vol.10 , Issue.2 , pp. 153-169
    • Auriault, J.L.1    Boutin, C.2
  • 3
    • 0001493942 scopus 로고    scopus 로고
    • Multiscale, hybrid mixture theory for swelling systems - I: Balance laws
    • DOI 10.1016/0020-7225(95)00089-5
    • L.S. Bennethum, and J.H. Cushman Multiscale, hybrid mixture theory for swelling systems - i: balance laws Int. J. Eng. Sci. 34 2 1996 125 145 (Pubitemid 126342987)
    • (1996) International Journal of Engineering Science , vol.34 , Issue.2 , pp. 125-145
    • Bennethum, L.S.1    Cushman, J.H.2
  • 4
    • 0001287609 scopus 로고    scopus 로고
    • Multiscale, hybrid mixture theory for swelling systems - II: Constitutive theory
    • DOI 10.1016/0020-7225(95)00090-9
    • L.S. Bennethum, and J.H. Cushman Multiscale, hybrid mixture theory for swelling systems - ii: constitutive theory Int. J. Eng. Sci. 34 2 1996 147 169 (Pubitemid 126342988)
    • (1996) International Journal of Engineering Science , vol.34 , Issue.2 , pp. 147-169
    • Bennethum, L.S.1    Cushman, J.H.2
  • 5
    • 0030884859 scopus 로고    scopus 로고
    • Modified Darcys law, Terzaghis effective stress principle and Ficks law for swelling clay soils
    • L.S. Bennethum, M.A. Murad, and J.H. Cushman Modified Darcys law, Terzaghis effective stress principle and Ficks law for swelling clay soils Comput. Geotechnics 20 34 1997 245 266
    • (1997) Comput. Geotechnics , vol.20 , Issue.34 , pp. 245-266
    • Bennethum, L.S.1    Murad, M.A.2    Cushman, J.H.3
  • 7
    • 0345643551 scopus 로고
    • General theory of three-dimensional consolidation
    • M.A. Biot General theory of three-dimensional consolidation J. Appl. Phys. 12 1941 155 164
    • (1941) J. Appl. Phys. , vol.12 , pp. 155-164
    • Biot, M.A.1
  • 8
    • 24944571072 scopus 로고
    • Theory of elasticity and consolidation for a porous anisotropic solid
    • M.A. Biot Theory of elasticity and consolidation for a porous anisotropic solid J. Appl. Phys. 26 2 1955 182 185
    • (1955) J. Appl. Phys. , vol.26 , Issue.2 , pp. 182-185
    • Biot, M.A.1
  • 9
    • 0032895922 scopus 로고    scopus 로고
    • Mechanotransduction in bone: Role of the lacuno-canalicular network
    • E.H. Burger, and J. Klein-Nulend Mechanotransduction in bone: role of the lacuno-canalicular network Faseb J. 13 1999 S101 S112
    • (1999) Faseb J. , vol.13
    • Burger, E.H.1    Klein-Nulend, J.2
  • 10
    • 0042909930 scopus 로고
    • Transient flow of slightly compressible fluids through double-porosity, double-permeability systems - A state-of-art review
    • Z.-X. Chen Transient flow of slightly compressible fluids through double-porosity, double-permeability systems - a state-of-art review Transp. Porous Media 4 1989 147 184
    • (1989) Transp. Porous Media , vol.4 , pp. 147-184
    • Chen, Z.-X.1
  • 11
    • 34848886826 scopus 로고    scopus 로고
    • On modelling the parallel diffusion flow in deforming porous media
    • DOI 10.1016/j.matcom.2007.01.034, PII S0378475407000274, Mathematical Modelling and Computational Methods in Applied Sciences and Engineering
    • R. Cimrman, and E. Rohan On modelling the parallel diffusion flow in deforming porous media Math. Comput. Simulation 76 2007 34 43 (Pubitemid 47503613)
    • (2007) Mathematics and Computers in Simulation , vol.76 , Issue.1-3 , pp. 34-43
    • Cimrman, R.1    Rohan, E.2
  • 12
    • 40049088779 scopus 로고    scopus 로고
    • The periodic unfolding method for perforated domains and Neumann sieve models
    • D. Cioranescu, A. Damlamian, G. Griso, and D. Onofrei The periodic unfolding method for perforated domains and Neumann sieve models J. Math. Pures Appl. 89 3 2008 248 277
    • (2008) J. Math. Pures Appl. , vol.89 , Issue.3 , pp. 248-277
    • Cioranescu, D.1    Damlamian, A.2    Griso, G.3    Onofrei, D.4
  • 13
    • 0038391423 scopus 로고    scopus 로고
    • Éclatement périodique et homogénéisation
    • DOI 10.1016/S1631-073X(02)02429-9, PII S1631073X02024299
    • D. Cioranescu, A. Damlamian, and G. Griso Periodic unfolding and homogenization C.R. Acad. Sci. Paris, Ser. I 335 2002 99 104 (Pubitemid 36645758)
    • (2002) Comptes Rendus Mathematique , vol.335 , Issue.1 , pp. 99-104
    • Cioranescu, D.1    Damlamian, A.2    Griso, G.3
  • 14
    • 67749122242 scopus 로고    scopus 로고
    • The periodic unfolding method in homogenization
    • D. Cioranescu, A. Damlamian, and G. Griso The periodic unfolding method in homogenization SIAM J. Math. Anal. 40 4 2008 1585 1620
    • (2008) SIAM J. Math. Anal. , vol.40 , Issue.4 , pp. 1585-1620
    • Cioranescu, D.1    Damlamian, A.2    Griso, G.3
  • 19
    • 69649093380 scopus 로고    scopus 로고
    • Hierarchical poroelasticity: Movement of interstitial fluid between levels in bones
    • S.C. Cowin, G. Gailani, and M. Benalla Hierarchical poroelasticity: movement of interstitial fluid between levels in bones Philos. Trans. R. Soc. A 367 2009 3401 3444
    • (2009) Philos. Trans. R. Soc. A , vol.367 , pp. 3401-3444
    • Cowin, S.C.1    Gailani, G.2    Benalla, M.3
  • 20
    • 0029395299 scopus 로고
    • A case for bone canaliculi as the anatomical site of strain generated potentials
    • S.C. Cowin, S. Weinbaum, and Y. Zeng A case for bone canaliculi as the anatomical site of strain generated potentials J. Biomech. 28 11 1995 1281 1297
    • (1995) J. Biomech. , vol.28 , Issue.11 , pp. 1281-1297
    • Cowin, S.C.1    Weinbaum, S.2    Zeng, Y.3
  • 21
    • 0032204927 scopus 로고    scopus 로고
    • The constitutive equations of finite strain poroelasticity in the light of a micro-macro approach
    • P. de Buhan, X. Chateau, and L. Dormieux The constitutive equations of finite strain poroelasticity in the light of a micro-macro approach Eur. J. Mech. A/solids 17 1998 909 921 (Pubitemid 128682415)
    • (1998) European Journal of Mechanics, A/Solids , vol.17 , Issue.6 , pp. 909-921
    • De Buhan, P.1    Chateau, X.2    Dormieux, L.3
  • 22
    • 36749067710 scopus 로고    scopus 로고
    • On the homogenization of a diffusion-deformation problem in strongly heterogeneous media
    • G. Griso, and E. Rohan On the homogenization of a diffusion-deformation problem in strongly heterogeneous media Ric. mat. 56 2007 161 188
    • (2007) Ric. Mat. , vol.56 , pp. 161-188
    • Griso, G.1    Rohan, E.2
  • 24
    • 17044419505 scopus 로고    scopus 로고
    • Modeling deformation-induced fluid flow in cortical bone's canalicular-lacunar system
    • DOI 10.1007/s10439-005-8959-6
    • S. Gururaja, H.J. Kim, C.C. Swan, R.A. Brand, and R.S. Lakes Modeling deformation-induced fluid flow in cortical bones lacunarcanalicular system Ann. Biomed. Eng. 33 2005 7 25 (Pubitemid 40496057)
    • (2005) Annals of Biomedical Engineering , vol.33 , Issue.1 , pp. 7-25
    • Gururaja, S.1    Kim, H.J.2    Swan, C.C.3    Brand, R.A.4    Lakes, R.S.5
  • 26
    • 0032212080 scopus 로고    scopus 로고
    • Differential effect of steady versus oscillating flow on bone cells
    • DOI 10.1016/S0021-9290(98)00114-6, PII S0021929098001146
    • C.R. Jacobs, C.E. Yellowley, B.R. Davis, Z. Zhou, J.M. Cimbala, and H.J. Donahue Differential effect of steady versus oscillating flow on bone cells J. Biomech. 31 11 1998 969 976 (Pubitemid 28561790)
    • (1998) Journal of Biomechanics , vol.31 , Issue.11 , pp. 969-976
    • Jacobs, C.R.1    Yellowley, C.E.2    Davis, B.R.3    Zhou, Z.4    Cimbala, J.M.5    Donahue, H.J.6
  • 27
    • 0141630244 scopus 로고    scopus 로고
    • "Whither flows the fluid in bone?" An osteocyte's perspective
    • DOI 10.1016/S0021-9290(03)00123-4
    • M.L. Knothe Tate Whither flows the fluid in bone? An osteocytes perspective J. Biomech. 36 2003 1409 1424 (Pubitemid 37120517)
    • (2003) Journal of Biomechanics , vol.36 , Issue.10 , pp. 1409-1424
    • Knothe Tate, M.L.1
  • 29
    • 32944464966 scopus 로고    scopus 로고
    • Multiscale analysis of the coupled effects governing the movement of interstitial fluid in cortical bone
    • DOI 10.1007/s10237-005-0009-7
    • T. Lemaire, S. Naili, and A. Rémond Multi-scale analysis of the coupled effects governing the movement of interstitial fluid in cortical bone Biomechan. Model. Mechanobiol. 5 2006 39 52 (Pubitemid 43261229)
    • (2006) Biomechanics and Modeling in Mechanobiology , vol.5 , Issue.1 , pp. 39-52
    • Lemaire, T.1    Naili, S.2    Remond, A.3
  • 30
    • 47149105069 scopus 로고    scopus 로고
    • Study of the influence of fibrous pericellular matrix in the cortical interstitial fluid movement
    • T. Lemaire, S. Naili, and A. Rémond Study of the influence of fibrous pericellular matrix in the cortical interstitial fluid movement J. Biomech. Eng. 130 2008 1 11
    • (2008) J. Biomech. Eng. , vol.130 , pp. 1-11
    • Lemaire, T.1    Naili, S.2    Rémond, A.3
  • 31
    • 0035089443 scopus 로고    scopus 로고
    • Numerical simulation of streaming potentials due to deformation-induced hierarchical flows in cortical bone
    • DOI 10.1115/1.1336796
    • A.F. Mak, and J.D. Zhang Numerical simulation of streaming potentials due to deformation-induced hierarchical flows in cortical bone J. Biomech. Eng. 123 1 2001 66 70 (Pubitemid 32202581)
    • (2001) Journal of Biomechanical Engineering , vol.123 , Issue.1 , pp. 66-70
    • Mak, A.F.T.1    Zhang, J.D.2
  • 32
    • 0031189473 scopus 로고    scopus 로고
    • A multiscale theory of swelling porous media: II. Dual porosity models for consolidation of clays incorporating physicochemical effects
    • M.A. Murad, and J.H. Cushman A multiscale theory of swelling porous media: II. Dual porosity models for consolidation of clays incorporating physicochemical effects Transp. Porous Media 28 1997 69 108
    • (1997) Transp. Porous Media , vol.28 , pp. 69-108
    • Murad, M.A.1    Cushman, J.H.2
  • 33
    • 0033874212 scopus 로고    scopus 로고
    • Thermomechanical theories for swelling porous media with microstructure
    • DOI 10.1016/S0020-7225(99)00054-3
    • M.A. Murad, and J.H. Cushman Thermomechanical theories for swelling porous media with microstructure Int. J. Eng. Sci. 38 2000 517 564 (Pubitemid 30540456)
    • (2000) International Journal of Engineering Science , vol.38 , Issue.5 , pp. 517-564
    • Murad, M.A.1    Cushman, J.H.2
  • 34
    • 0035808189 scopus 로고    scopus 로고
    • Micromechanical computational modeling of secondary consolidation and hereditary creep in soils
    • DOI 10.1016/S0045-7825(00)00218-8, PII S0045782500002188
    • M.A. Murad, J.N. Guerreiro, and A.F.D. Loula Micromechanical computational modeling of secondary consolidation and hereditary creep in soils Comput. Methods Appl. Mech. Eng. 190 2001 1985 2016 (Pubitemid 32333694)
    • (2001) Computer Methods in Applied Mechanics and Engineering , vol.190 , Issue.15-17 , pp. 1985-2016
    • Murad, M.A.1    Guerreiro, J.N.2    Loula, A.F.D.3
  • 36
    • 0017654342 scopus 로고
    • Transport mechanism operating between blood supply and osteocytes in long bones
    • DOI 10.1038/269080a0
    • K. Piekarski, and M. Munro Transport mechanism operating between blood supply and osteocytes in long bones Nature 269 1977 80 82 (Pubitemid 8160686)
    • (1977) Nature , vol.269 , Issue.5623 , pp. 80-82
    • Piekarski, K.1    Munro, M.2
  • 37
    • 0021592452 scopus 로고
    • An anatomical model for streaming potentials in osteons
    • S. Pollack, N. Petrov, R. Salzstein, G. Brankov, and R. Blagoeva An anatomical model for streaming potentials in osteons J. Biomech. 17 1984 627 636 (Pubitemid 14038372)
    • (1984) Journal of Biomechanics , vol.17 , Issue.8 , pp. 627-636
    • Pollack, S.R.1    Petrov, N.2    Salzstein, R.3
  • 38
    • 3242719599 scopus 로고    scopus 로고
    • Cylindre transverse isotrope poroélastique chargé cycliquement: Application a un ostéon
    • DOI 10.1016/j.crme.2004.05.001, PII S1631072104001378
    • A. Rémond, and S. Naili Cyclic loading of a transverse isotropic poroelastic cylinder: a model for the osteon C.R. Mec. 332 9 2004 759 766 (Pubitemid 38950677)
    • (2004) Comptes Rendus - Mecanique , vol.332 , Issue.9 , pp. 759-766
    • Remond, A.1    Naili, S.2
  • 39
    • 22944488857 scopus 로고    scopus 로고
    • Transverse isotropic poroelastic osteon model under cyclic loading
    • DOI 10.1016/j.mechrescom.2004.10.003, PII S0093641304001053
    • A. Rémond, and S. Naili Transverse isotropic poroelastic osteon model under cyclic loading Mech. Res. Commun. 32 6 2005 645 651 (Pubitemid 41042532)
    • (2005) Mechanics Research Communications , vol.32 , Issue.6 , pp. 645-651
    • Remond, A.1    Naili, S.2
  • 40
    • 54649085074 scopus 로고    scopus 로고
    • Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: A finite element study
    • A. Rémond, S. Naili, and T. Lemaire Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study Biomech. Model. Mechanobiol. 7 2008 487 495
    • (2008) Biomech. Model. Mechanobiol. , vol.7 , pp. 487-495
    • Rémond, A.1    Naili, S.2    Lemaire, T.3
  • 41
    • 0037472513 scopus 로고    scopus 로고
    • Sensitivity strategies in modelling heterogeneous media undergoing finite deformation
    • E. Rohan Sensitivity strategies in modelling heterogeneous media undergoing finite deformation Math. Comput. Simulation 61 36 2003 261 270
    • (2003) Math. Comput. Simulation , vol.61 , Issue.36 , pp. 261-270
    • Rohan, E.1
  • 42
    • 84857917978 scopus 로고    scopus 로고
    • Homogenization approach to the multi-compartment model of perfusion
    • E. Rohan Homogenization approach to the multi-compartment model of perfusion Proc. Appl. Math. Mech. 6 2006 79 82
    • (2006) Proc. Appl. Math. Mech. , vol.6 , pp. 79-82
    • Rohan, E.1
  • 43
    • 33747192844 scopus 로고    scopus 로고
    • Modeling large-deformation-induced microflow in soft biological tissues
    • DOI 10.1007/s00162-006-0020-3
    • E. Rohan Modelling large deformation induced microflow in soft biological tissues Theor. Comput. Fluid Dyn. 20 2006 251 276 (Pubitemid 44230386)
    • (2006) Theoretical and Computational Fluid Dynamics , vol.20 , Issue.4 , pp. 251-276
    • Rohan, E.1
  • 44
    • 77949635103 scopus 로고    scopus 로고
    • Two-scale modelling of tissue perfusion problem using homogenization of dual porous media
    • E. Rohan, and R. Cimrman Two-scale modelling of tissue perfusion problem using homogenization of dual porous media Int. J. Multiscale Comput. Eng. 8 2010 81 102
    • (2010) Int. J. Multiscale Comput. Eng. , vol.8 , pp. 81-102
    • Rohan, E.1    Cimrman, R.2
  • 45
    • 84865707813 scopus 로고    scopus 로고
    • Multiscale FE simulation of diffusion-deformation processes in homogenized dual-porous media
    • in press, doi
    • Rohan, E., Cimrman, R. Multiscale FE simulation of diffusion-deformation processes in homogenized dual-porous media. Math. Comput. Simulation, in press, doi: 10.1016/j.matcom.2011.02.011.
    • Math. Comput. Simulation
    • Rohan, E.1    Cimrman, R.2
  • 49
    • 0028386524 scopus 로고
    • A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses
    • DOI 10.1016/0021-9290(94)90010-8
    • S. Weinbaum, S.C. Cowin, and Y. Zeng A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses J. Biomech. 27 1994 339 360 (Pubitemid 24061729)
    • (1994) Journal of Biomechanics , vol.27 , Issue.3 , pp. 339-360
    • Weinbaum, S.1
  • 50
    • 48549106928 scopus 로고    scopus 로고
    • Two-scale, three-phase theory for swelling drug delivery systems. Part ii: Flow and transport models
    • T. Weinstein, L.S. Bennethum, and J.H. Cushman Two-scale, three-phase theory for swelling drug delivery systems. Part ii: flow and transport models J. Pharm. Sci. 97 5 2007 1904 1915
    • (2007) J. Pharm. Sci. , vol.97 , Issue.5 , pp. 1904-1915
    • Weinstein, T.1    Bennethum, L.S.2    Cushman, J.H.3
  • 53
    • 0034792594 scopus 로고    scopus 로고
    • A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix
    • DOI 10.1016/S0021-9290(01)00107-5, PII S0021929001001075
    • L. You, S.C. Cowin, M.B. Schaffler, and S. Weinbaum A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix J. Biomech. 34 2001 1375 1386 (Pubitemid 32970752)
    • (2001) Journal of Biomechanics , vol.34 , Issue.11 , pp. 1375-1386
    • You, L.1    Cowin, S.C.2    Schaffler, M.B.3    Weinbaum, S.4
  • 54
    • 0032331189 scopus 로고    scopus 로고
    • On the calculation of bone pore water pressure due to mechanical loading
    • D. Zhang, S. Weinbaum, and S. Cowin On the calculation of bone pore water pressure due to mechanical loading Int. J. Solids Struct. 35 3435 1998 4981 4997
    • (1998) Int. J. Solids Struct. , vol.35 , Issue.3435 , pp. 4981-4997
    • Zhang, D.1    Weinbaum, S.2    Cowin, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.