메뉴 건너뛰기




Volumn 7, Issue 47, 2010, Pages 955-966

Nonlinear elasticity of biological tissues with statistical fibre orientation

Author keywords

Articular cartilage; Biological tissue; Composite material; Fibre reinforced; Statistical orientation

Indexed keywords

BIOLOGICAL MATERIALS; CARTILAGE; COMPOSITE MICROMECHANICS; DEFORMATION; ELASTICITY; FIBERS; HISTOLOGY; INTEGRATION; JOINTS (ANATOMY); LIGAMENTS; PROBABILITY DENSITY FUNCTION; SPHERES; ULTRASONIC MEASUREMENT;

EID: 77953149044     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2009.0502     Document Type: Article
Times cited : (122)

References (46)
  • 1
    • 56349098742 scopus 로고    scopus 로고
    • Validation of finite element predictions of cartilage contact pressure in the human hip joint
    • doi:10.1115/1.2953472
    • Anderson, A., Ellis, B., Maas, S., Peters, C. & Weiss, J. 2008 Validation of finite element predictions of cartilage contact pressure in the human hip joint. J. Biomech. Eng. 130, 051 008. (doi:10.1115/1.2953472)
    • (2008) J. Biomech. Eng. , vol.130 , pp. 051008
    • Anderson, A.1    Ellis, B.2    Maas, S.3    Peters, C.4    Weiss, J.5
  • 2
    • 0034143877 scopus 로고    scopus 로고
    • Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp-Part I: Experimental results
    • doi:10.1115/1.429624
    • Billiar, K. L. & Sacks, M. S. 2000 Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp-Part I: experimental results. J. Biomech. Eng. 122, 23-30. (doi:10.1115/1.429624)
    • (2000) J. Biomech. Eng. , vol.122 , pp. 23-30
    • Billiar, K.L.1    Sacks, M.S.2
  • 3
    • 33745463261 scopus 로고    scopus 로고
    • Microplane constitutive model and computational framework for blood vessel tissue
    • doi:10.1115/1.2187036
    • Caner, F. & Carol, I. 2006 Microplane constitutive model and computational framework for blood vessel tissue. J. Biomech. Eng. 128, 419-427. (doi:10.1115/1.2187036)
    • (2006) J. Biomech. Eng. , vol.128 , pp. 419-427
    • Caner, F.1    Carol, I.2
  • 4
    • 85047676877 scopus 로고
    • Measurements from light and polarised light microscopy of human coronary arteries fixed at distending pressure
    • doi:10.1093/cvr/23.11.973
    • Canham, P. B., Finlay, H. M., Dixon, J. G., Boughner, D. R. & Chen, A. 1989 Measurements from light and polarised light microscopy of human coronary arteries fixed at distending pressure. Cardiovasc. Res. 23, 973-982. (doi:10.1093/cvr/23.11.973)
    • (1989) Cardiovasc. Res. , vol.23 , pp. 973-982
    • Canham, P.B.1    Finlay, H.M.2    Dixon, J.G.3    Boughner, D.R.4    Chen, A.5
  • 5
    • 0028756152 scopus 로고
    • Conewise linear elastic materials
    • doi:10.1007/BF00043417
    • Curnier, A., He, Q.-C. & Zysset, P. 1995 Conewise linear elastic materials. J. Elasticity 37, 1-38. (doi:10.1007/BF00043417)
    • (1995) J. Elasticity , vol.37 , pp. 1-38
    • Curnier, A.1    He, Q.-C.2    Zysset, P.3
  • 6
    • 77956760323 scopus 로고    scopus 로고
    • Volumetric-distortional decomposition of deformation and elasticity tensor
    • In press. doi:10.1177/1081286509105591
    • Federico, S. In press. Volumetric-distortional decomposition of deformation and elasticity tensor. Math. Mech. Solids. (doi:10.1177/ 1081286509105591)
    • Math. Mech. Solids.
    • Federico, S.1
  • 7
    • 50149106804 scopus 로고    scopus 로고
    • On the anisotropy and inhomogeneity of permeability in articular cartilage
    • doi:10.1007/s10237-007-0091-0
    • Federico, S. & Herzog, W. 2008a On the anisotropy and inhomogeneity of permeability in articular cartilage. Biomech. Model. Mechanobiol. 7, 367-378. (doi:10.1007/s10237-007-0091-0)
    • (2008) Biomech. Model. Mechanobiol. , vol.7 , pp. 367-378
    • Federico, S.1    Herzog, W.2
  • 8
    • 38749104232 scopus 로고    scopus 로고
    • On the permeability of fibre-reinforced porous materials
    • doi:10.1016/j.ijsolstr.2007.11.014
    • Federico, S. & Herzog, W. 2008b On the permeability of fibre-reinforced porous materials. Int. J. Solids Struct. 45, 2160-2172. (doi:10.1016/j.ijsolstr.2007.11.014)
    • (2008) Int. J. Solids Struct. , vol.45 , pp. 2160-2172
    • Federico, S.1    Herzog, W.2
  • 9
    • 56549110892 scopus 로고    scopus 로고
    • Towards an analytical model of soft tissues
    • doi:10.1016/j.jbiomech.2008.05.039
    • Federico, S. & Herzog, W. 2008c Towards an analytical model of soft tissues. J. Biomech. 41, 3309-3313. (doi:10.1016/j.jbiomech.2008.05.039)
    • (2008) J. Biomech. , vol.41 , pp. 3309-3313
    • Federico, S.1    Herzog, W.2
  • 10
    • 4544289390 scopus 로고    scopus 로고
    • A transversely isotropic composite with a statistical distribution of spheroidal inclusions: A geometrical approach to overall properties
    • doi:10.1016/j.jmps.2004.03.010
    • Federico, S., Grillo, A. & Herzog, W. 2004 A transversely isotropic composite with a statistical distribution of spheroidal inclusions: a geometrical approach to overall properties. J. Mech. Phys. Solids 52, 2309-2327. (doi:10.1016/j.jmps.2004.03.010)
    • (2004) J. Mech. Phys. Solids , vol.52 , pp. 2309-2327
    • Federico, S.1    Grillo, A.2    Herzog, W.3
  • 11
    • 0006280110 scopus 로고
    • Thermodynamic relations for highly elastic materials
    • doi:10.1039/tf9615700829
    • Flory, P. J. 1961 Thermodynamic relations for highly elastic materials. Trans. Faraday Soc. 57, 829-838. (doi:10.1039/tf9615700829)
    • (1961) Trans. Faraday Soc. , vol.57 , pp. 829-838
    • Flory, P.J.1
  • 12
    • 0037368561 scopus 로고    scopus 로고
    • Dynamic measurement of internal solid displacement in articular cartilage using ultrasound backscatter
    • DOI 10.1016/S0021-9290(02)00413-X
    • Fortin, M., Buschmann, M. D., Bertrand, M. J., Foster, F. S. & Ophir, J. 2003 Dynamic measurement of internal solid displacement in articular cartilage using ultrasound backscatter. J. Biomech. 36, 443-447. (doi:10.1016/S0021-9290(02)00413-X) (Pubitemid 36197682)
    • (2003) Journal of Biomechanics , vol.36 , Issue.3 , pp. 443-447
    • Fortin, M.1    Buschmann, M.D.2    Bertrand, M.J.3    Foster, F.S.4    Ophir, J.5
  • 14
    • 0036815599 scopus 로고    scopus 로고
    • A rate-independent elastoplastic constitutive model for (biological) fiberreinforced composites at finite strains: Continuum basis, algorithmic formulation and finite element implementation
    • doi:10.1007/s00466-002-0347-6
    • Gasser, T. C. & Holzapfel, G. A. 2002 A rate-independent elastoplastic constitutive model for (biological) fiberreinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation. Comput. Mech. 29, 340-360. (doi:10.1007/s00466-002-0347-6)
    • (2002) Comput. Mech. , vol.29 , pp. 340-360
    • Gasser, T.C.1    Holzapfel, G.A.2
  • 15
    • 33745171176 scopus 로고    scopus 로고
    • Hyperelastic modelling of arterial layers with distributed collagen fibre orientations
    • doi:10.1098/rsif.2005.0073
    • Gasser, T. C., Ogden, R. W. & Holzapfel, G. A. 2006 Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3, 15-35. (doi:10.1098/rsif.2005.0073)
    • (2006) J. R. Soc. Interface , vol.3 , pp. 15-35
    • Gasser, T.C.1    Ogden, R.W.2    Holzapfel, G.A.3
  • 17
    • 33745180485 scopus 로고    scopus 로고
    • A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus
    • doi:10.1016/j.jmps.2006.02.006
    • Guo, Z. Y., Peng, X. Q. & Moran, B. 2006 A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. J. Mech. Phys. Solids 54, 1952-1971. (doi:10.1016/j.jmps.2006. 02.006)
    • (2006) J. Mech. Phys. Solids , vol.54 , pp. 1952-1971
    • Guo, Z.Y.1    Peng, X.Q.2    Moran, B.3
  • 18
    • 42649092875 scopus 로고    scopus 로고
    • On constitutive modelling of porous neo-Hookean composites
    • doi:10.1016/j.jmps.2007.12.007
    • Guo, Z. Y., Caner, F., Peng, X. Q. & Moran, B. 2008 On constitutive modelling of porous neo-Hookean composites. J. Mech. Phys. Solids 56, 2338-2357. (doi:10.1016/j.jmps.2007.12.007)
    • (2008) J. Mech. Phys. Solids , vol.56 , pp. 2338-2357
    • Guo, Z.Y.1    Caner, F.2    Peng, X.Q.3    Moran, B.4
  • 19
    • 0030528002 scopus 로고    scopus 로고
    • McLaren's improved snub cube and other new spherical designs in three dimensions
    • doi:10.1007/BF02711518
    • Hardin, R. H. & Sloane, N. J. A. 1996 McLaren's improved snub cube and other new spherical designs in three dimensions. Discrete Comput. Geom. 15, 429-441. (doi:10.1007/BF02711518)
    • (1996) Discrete Comput. Geom. , vol.15 , pp. 429-441
    • Hardin, R.H.1    Sloane, N.J.A.2
  • 21
    • 0035946893 scopus 로고    scopus 로고
    • A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computional aspects and applications
    • doi:10.1016/S0045-7825(00)00323-6
    • Holzapfel, G. A. & Gasser, T. C. 2001 A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computional aspects and applications. Comput. Meth. Appl. Mech. Eng. 190, 4379-4403. (doi:10.1016/S0045-7825(00)00323-6)
    • (2001) Comput. Meth. Appl. Mech. Eng. , vol.190 , pp. 4379-4403
    • Holzapfel, G.A.1    Gasser, T.C.2
  • 22
    • 0034434740 scopus 로고    scopus 로고
    • A new constitutive framework for arterial wall mechanics and a comparative study of material models
    • doi:10.1023/A:1010835316564
    • Holzapfel, G. A., Gasser, T. C. & Ogden, R. W. 2000 A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elasticity 61, 1-48. (doi:10.1023/A:1010835316564)
    • (2000) J. Elasticity , vol.61 , pp. 1-48
    • Holzapfel, G.A.1    Gasser, T.C.2    Ogden, R.W.3
  • 23
    • 0031281833 scopus 로고    scopus 로고
    • A structurally based stress-stretch relationship for tendon and ligament
    • doi:10.1115/1.2798284
    • Hurschler, C., Loitz-Ramage, B. & Vanderby Jr, R. 1997 A structurally based stress-stretch relationship for tendon and ligament. J. Biomech. Eng. 119, 392-399. (doi:10.1115/1.2798284)
    • (1997) J. Biomech. Eng. , vol.119 , pp. 392-399
    • Hurschler, C.1    Loitz-Ramage, B.2    Vanderby Jr., R.3
  • 24
    • 0020586767 scopus 로고
    • Constitutive equations for fibrous connective tissues
    • Lanir, Y. 1983 Constitutive equations for fibrous connective tissues. J. Biomech. 16, 1-12. (doi:10.1016/0021-9290(83)90041-6) (Pubitemid 13125809)
    • (1983) Journal of Biomechanics , vol.16 , Issue.1 , pp. 1-12
    • Lanir, Y.1
  • 25
    • 0742304324 scopus 로고    scopus 로고
    • Strain-rate dependence of cartilage stiffness in unconfined compression: The role of fibril reinforcement versus tissue volume change in fluid pressurization
    • DOI 10.1016/S0021-9290(03)00263-X
    • Li, L. & Herzog, W. 2004 Strain-rate dependence of cartilage stiffness in unconfined compression: the role of fibril reinforcement versus tissue volume change in fluid pressurization. J. Biomech. 37, 375-382. (doi:10.1016/S0021-9290(03)00263-X) (Pubitemid 38156085)
    • (2004) Journal of Biomechanics , vol.37 , Issue.3 , pp. 375-382
    • Li, L.P.1    Herzog, W.2
  • 27
    • 56949107109 scopus 로고    scopus 로고
    • Towards an orientation-distribution-based multi-scale approach for remodelling biological tissues
    • doi:10.1080/10255840701771776
    • Menzel, A., Harrysson, M. & Ristinmaa, M. 2008 Towards an orientation-distribution-based multi-scale approach for remodelling biological tissues. Comput. Meth. Biomech. Biomed. Eng. 11, 505-524. (doi:10.1080/ 10255840701771776)
    • (2008) Comput. Meth. Biomech. Biomed. Eng. , vol.11 , pp. 505-524
    • Menzel, A.1    Harrysson, M.2    Ristinmaa, M.3
  • 28
    • 0028445932 scopus 로고
    • Aspects of the formulation and finite element implementation of large strain isotropic elasticity
    • doi:10.1002/nme.1620371202
    • Miehe, C. 1994 Aspects of the formulation and finite element implementation of large strain isotropic elasticity. Int. J. Numer. Meth. Eng. 37, 1981-2004. (doi:10.1002/nme.1620371202)
    • (1994) Int. J. Numer. Meth. Eng. , vol.37 , pp. 1981-2004
    • Miehe, C.1
  • 29
    • 0347659487 scopus 로고    scopus 로고
    • X-ray diffraction of the molecular substructure of human articular cartilage
    • doi:10.1080/714040519
    • Mollenhauer, J., Aurich, M., Muehleman, C., Khelashvilli, G. & Irving,T.C. 2003X-ray diffraction of the molecular substructure of human articular cartilage. Conn. Tiss. Res. 44, 201-207. (doi:10.1080/714040519)
    • (2003) Conn. Tiss. Res. , vol.44 , pp. 201-207
    • Mollenhauer, J.1    Aurich, M.2    Muehleman, C.3    Khelashvilli, G.4    Irving, T.C.5
  • 30
    • 0017933312 scopus 로고
    • Nearly isochoric elastic deformations: Application to rubberlike solids
    • doi:10.1016/0022-5096(78)90012-1
    • Ogden, R. W. 1978 Nearly isochoric elastic deformations: application to rubberlike solids. J. Mech. Phys. Solids 26, 37-57. (doi:10.1016/0022-5096(78) 90012-1)
    • (1978) J. Mech. Phys. Solids , vol.26 , pp. 37-57
    • Ogden, R.W.1
  • 31
    • 1642432048 scopus 로고    scopus 로고
    • Mechanical response of bovine articular cartilage under dynamic unconfined compression loading at physiological stress levels
    • DOI 10.1016/j.joca.2003.08.005
    • Park, S., Hung, C. T. & Ateshian, G. A. 2004 Mechanical response of bovine articular cartilage under dynamic unconfined compression loading at physiological stress levels. Osteoarthr. Cartilage 12, 65-73. (doi:10.1016/j.joca.2003.08.005) (Pubitemid 38111552)
    • (2004) Osteoarthritis and Cartilage , vol.12 , Issue.1 , pp. 65-73
    • Park, S.1    Hung, C.T.2    Ateshian, G.A.3
  • 32
    • 34547401038 scopus 로고    scopus 로고
    • The importance of the compatibility of nonlinear constitutive theories with their linear counterparts
    • doi:10.1115/1.2338053
    • Quintanilla, R. & Saccomandi, G. 2007 The importance of the compatibility of nonlinear constitutive theories with their linear counterparts. J. Appl. Mech. 74, 455-460. (doi:10.1115/1.2338053)
    • (2007) J. Appl. Mech. , vol.74 , pp. 455-460
    • Quintanilla, R.1    Saccomandi, G.2
  • 33
    • 0037397670 scopus 로고    scopus 로고
    • Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues
    • doi:10.1115/1.1544508
    • Sacks, M. S. 2003 Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. J. Biomech. Eng. 125, 280-287. (doi:10.1115/1.1544508)
    • (2003) J. Biomech. Eng. , vol.125 , pp. 280-287
    • Sacks, M.S.1
  • 34
    • 36549025820 scopus 로고    scopus 로고
    • On the physical assumptions underlying the volumetric-isochoric split and the case of anisotropy
    • doi:10.1016/j.euromechsol.2007.04.001
    • Sansour, C. 2008 On the physical assumptions underlying the volumetric-isochoric split and the case of anisotropy. Eur. J. Mech. A/Solids 27, 28-39. (doi:10.1016/j.euromechsol.2007.04.001)
    • (2008) Eur. J. Mech. A/Solids , vol.27 , pp. 28-39
    • Sansour, C.1
  • 35
    • 0026103678 scopus 로고
    • Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms
    • doi:10.1016/0045-7825(91)90100-K
    • Simo, J. C. & Taylor, R. L. 1991 Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms. Comput. Meth. Appl. Mech. Eng. 85, 273-310. (doi:10.1016/0045-7825(91)90100-K)
    • (1991) Comput. Meth. Appl. Mech. Eng. , vol.85 , pp. 273-310
    • Simo, J.C.1    Taylor, R.L.2
  • 36
    • 46549096707 scopus 로고
    • Variational and projection methods for the volume constraint in finite deformation elasto-plasticity
    • doi:10.1016/0045-7825(85)90033-7
    • Simo, J. C., Taylor, R. L. & Pister, K. S. 1985 Variational and projection methods for the volume constraint in finite deformation elasto-plasticity. Comput. Meth. Appl. Mech. Eng. 51, 177-208. (doi:10.1016/0045-7825(85)90033-7)
    • (1985) Comput. Meth. Appl. Mech. Eng. , vol.51 , pp. 177-208
    • Simo, J.C.1    Taylor, R.L.2    Pister, K.S.3
  • 37
    • 0032983690 scopus 로고    scopus 로고
    • A fibril-network-reinforced biphasic model of cartilage in unconfined compression
    • doi:10.1115/1.2798330
    • Soulhat, J., Buschmann, M. D. & Shirazi-Adl, A. 1999 A fibril-network-reinforced biphasic model of cartilage in unconfined compression. J. Biomech. Eng. 121, 340-347. (doi:10.1115/1.2798330)
    • (1999) J. Biomech. Eng. , vol.121 , pp. 340-347
    • Soulhat, J.1    Buschmann, M.D.2    Shirazi-Adl, A.3
  • 39
    • 0019677390 scopus 로고
    • Elastic behavior of composite materials: Theoretical foundations
    • doi:10.1016/S0065-2156(08)70332-6
    • Walpole, L. J. 1981 Elastic behavior of composite materials: theoretical foundations. Adv. Appl. Mech. 21, 169-242. (doi:10.1016/S0065-2156(08)70332-6)
    • (1981) Adv. Appl. Mech. , vol.21 , pp. 169-242
    • Walpole, L.J.1
  • 41
    • 0035187725 scopus 로고    scopus 로고
    • Computational modeling of ligament mechanics
    • Weiss, J. A. & Gardiner, J. C. 2001 Computational modeling of ligament mechanics. Crit. Rev. Biomed. Eng. 29, 303-371.
    • (2001) Crit. Rev. Biomed. Eng. , vol.29 , pp. 303-371
    • Weiss, J.A.1    Gardiner, J.C.2
  • 42
    • 0030213907 scopus 로고    scopus 로고
    • Finite element implementation of incompressible, transversely isotropic hyperelasticity
    • doi:10.1016/0045-7825(96)01035-3
    • Weiss, J. A., Maker, B. N. & Govindjee, S. 1996 Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput. Meth. Appl. Mech. Eng. 135, 107-128. (doi:10.1016/0045-7825(96)01035-3)
    • (1996) Comput. Meth. Appl. Mech. Eng. , vol.135 , pp. 107-128
    • Weiss, J.A.1    Maker, B.N.2    Govindjee, S.3
  • 43
    • 85020778215 scopus 로고    scopus 로고
    • See
    • Weisstein, E. W. 2005 Erfi. From MathWorld-A Wolfram Web Resource. See http://mathworld.wolfram.com/Erfi.html.
    • (2005) Erfi
    • Weisstein, E.W.1
  • 45
    • 0842286650 scopus 로고    scopus 로고
    • Stresses in the local collagen network of articular cartilage: A poroviscoelastic fibril-reinforced finite element study
    • doi:10.1016/S0021-9290(03)00267-7
    • Wilson,W., van Donkelaar, C. C., van Rietbergen, B., Ito, K.& Huiskes, R. 2004 Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study. J. Biomech. 37, 357-366. (doi:10.1016/S0021-9290(03)00267-7)
    • (2004) J. Biomech. , vol.37 , pp. 357-366
    • Wilson, W.1    Van Donkelaar, C.C.2    Van Rietbergen, B.3    Ito, K.4    Huiskes, R.5
  • 46
    • 77953141083 scopus 로고    scopus 로고
    • Wolfram Research Champaign, IL: Wolfram Research, Inc.
    • Wolfram Research 2008 Mathematica 6.0-documentation. Champaign, IL: Wolfram Research, Inc.
    • (2008) Mathematica 6.0-documentation


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.