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Volumn 81, Issue 2, 2010, Pages 189-206

Numerical integration on the sphere and its effect on the material symmetry of constitutive equations - A comparative study

Author keywords

Anisotropy; Constitutive equations; Microplane models; Microsphere models; Numerical integration; Solids

Indexed keywords

COMPARATIVE STUDIES; EXPONENTIAL MODELS; FINITE ELEMENT CALCULATIONS; FULL NETWORK MODEL; INTEGRATION POINTS; INTEGRATION SCHEME; MATERIAL SYMMETRY; MICRO-SPHERE MODEL; MICROPLANE MODELS; NON-LINEAR; NUMBER OF INTEGRATIONS; NUMERICAL ERRORS; NUMERICAL EXAMPLE; NUMERICAL INTEGRATION; NUMERICAL INTEGRATIONS; RIGID ROTATION; RUBBER ELASTICITY; SOFT TISSUE; STRONG ANISOTROPY; SYMMETRY PROPERTIES;

EID: 73149088599     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2688     Document Type: Article
Times cited : (97)

References (53)
  • 1
    • 0018385567 scopus 로고
    • A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues
    • Lanir Y. A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues. Journal of Biomechanics 1979; 12(6):423-436.
    • (1979) Journal of Biomechanics , vol.12 , Issue.6 , pp. 423-436
    • Lanir, Y.1
  • 2
    • 0020586767 scopus 로고
    • Constitutive equations for fibrous connective tissues
    • Lanir Y. Constitutive equations for fibrous connective tissues. Journal of Biomechanics 1983; 16(1):1-2.
    • (1983) Journal of Biomechanics , vol.16 , Issue.1 , pp. 1-2
    • Lanir, Y.1
  • 3
    • 0037397670 scopus 로고    scopus 로고
    • Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues
    • Sacks MS. Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. Journal of Biomechanical Engineering 2003; 125(2):280-287.
    • (2003) Journal of Biomechanical Engineering , vol.125 , Issue.2 , pp. 280-287
    • Sacks, M.S.1
  • 4
    • 0033804203 scopus 로고    scopus 로고
    • Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: Part Ia structural constitutive model
    • Billiar KL, Sacks MS. Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: part Ia structural constitutive model. Journal of Biomechanical Engineering 2000; 122(4):327-335.
    • (2000) Journal of Biomechanical Engineering , vol.122 , Issue.4 , pp. 327-335
    • Billiar, K.L.1    Sacks, M.S.2
  • 5
    • 18444380076 scopus 로고    scopus 로고
    • A structural constitutive model for collagenous cardiovascular tissues incorporating the angular fiber distribution
    • Driessen NJB, Bouten CVC, Baaijens FPT. A structural constitutive model for collagenous cardiovascular tissues incorporating the angular fiber distribution. Journal of Biomechanical Engineering 2005; 127(3):494-503.
    • (2005) Journal of Biomechanical Engineering , vol.127 , Issue.3 , pp. 494-503
    • Driessen, N.J.B.1    Bouten, C.V.C.2    Baaijens, F.P.T.3
  • 6
    • 33745171176 scopus 로고    scopus 로고
    • Hyperelastic modelling of arterial layers with distributed collagen fibre orientations
    • Gasser TC, Ogden RW, Holzapfel GA. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. Journal of the Royal Society Interface 2006; 3(6):15-35.
    • (2006) Journal of The Royal Society Interface , vol.3 , Issue.6 , pp. 15-35
    • Gasser, T.C.1    Ogden, R.W.2    Holzapfel, G.A.3
  • 7
    • 33745463261 scopus 로고    scopus 로고
    • Microplane constitutive model and computational framework for blood vessel tissue
    • Caner FC, Carol I. Microplane constitutive model and computational framework for blood vessel tissue. Journal of Biomechanical Engineering 2006; 128(3):419-427.
    • (2006) Journal of Biomechanical Engineering , vol.128 , Issue.3 , pp. 419-427
    • Caner, F.C.1    Carol, I.2
  • 11
    • 36849118054 scopus 로고
    • Theory of the elastic properties of rubber
    • James HM, Guth E. Theory of the elastic properties of rubber. The Journal of Chemical Physics 1943; 11(10): 455-481.
    • (1943) The Journal of Chemical Physics , vol.11 , Issue.10 , pp. 455-481
    • James, H.M.1    Guth, E.2
  • 12
    • 0009317350 scopus 로고
    • Statistical mechanics of cross-linked polymer networks I. Rubberlike elasticity
    • Flory PJ, Rehner J. Statistical mechanics of cross-linked polymer networks I. Rubberlike elasticity. The Journal of Chemical Physics 1943; 11(11):512-520.
    • (1943) The Journal of Chemical Physics , vol.11 , Issue.11 , pp. 512-520
    • Flory, P.J.1    Rehner, J.2
  • 13
    • 0041097550 scopus 로고
    • A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials
    • Arruda EM, Boyce MC. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids 1993; 41(2):389-412.
    • (1993) Journal of The Mechanics and Physics of Solids , vol.41 , Issue.2 , pp. 389-412
    • Arruda, E.M.1    Boyce, M.C.2
  • 14
    • 34347098764 scopus 로고
    • Beziehung zwischen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer Stoffe
    • Kuhn W, Grün F. Beziehung zwischen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer Stoffe. Kolloid Zeitschrift 1942; 101(3):248-271.
    • (1942) Kolloid Zeitschrift , vol.101 , Issue.3 , pp. 248-271
    • Kuhn, W.1    Grün, F.2
  • 17
    • 0000768173 scopus 로고
    • On improved 3-D non-Gaussian network models for rubber elasticity
    • Wu PD, van der Giessen E. On improved 3-D non-Gaussian network models for rubber elasticity. Mechanics Research Communications 1992; 19(5):427-433.
    • (1992) Mechanics Research Communications , vol.19 , Issue.5 , pp. 427-433
    • Wu, P.D.1    van der Giessen, E.2
  • 18
    • 0027559646 scopus 로고
    • On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers
    • Wu PD, van der Giessen E. On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers. Journal of the Mechanics and Physics of Solids 1993; 41(3):427-456.
    • (1993) Journal of The Mechanics and Physics of Solids , vol.41 , Issue.3 , pp. 427-456
    • Wu, P.D.1    van der Giessen, E.2
  • 19
    • 4544245878 scopus 로고    scopus 로고
    • A micro-macro approach to rubber-like materials. Part I: The non-affine micro-sphere model of rubber elasticity
    • Miehe C, Göktepe S, Lulei F. A micro-macro approach to rubber-like materials. Part I: the non-affine micro-sphere model of rubber elasticity. Journal of the Mechanics and Physics of Solids 2004; 52(11):2617-2660.
    • (2004) Journal of The Mechanics and Physics of Solids , vol.52 , Issue.11 , pp. 2617-2660
    • Miehe, C.1    Göktepe, S.2    Lulei, F.3
  • 20
    • 23844545370 scopus 로고    scopus 로고
    • A micro-macro approach to rubber-like materials. Part II: The micro-sphere model of finite rubber viscoelasticity
    • Miehe C, Göktepe S. A micro-macro approach to rubber-like materials. Part II: the micro-sphere model of finite rubber viscoelasticity. Journal of the Mechanics and Physics of Solids 2005; 53(10):2231-2258.
    • (2005) Journal of The Mechanics and Physics of Solids , vol.53 , Issue.10 , pp. 2231-2258
    • Miehe, C.1    Göktepe, S.2
  • 21
    • 23844500813 scopus 로고    scopus 로고
    • A micro-macro approach to rubber-like materials. Part III: The micro-sphere model of anisotropic Mullins-type damage
    • Göktepe S, Miehe C. A micro-macro approach to rubber-like materials. Part III: the micro-sphere model of anisotropic Mullins-type damage. Journal of the Mechanics and Physics of Solids 2005; 53(10):2259-2283.
    • (2005) Journal of The Mechanics and Physics of Solids , vol.53 , Issue.10 , pp. 2259-2283
    • Göktepe, S.1    Miehe, C.2
  • 22
    • 33646770347 scopus 로고    scopus 로고
    • A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy
    • Diani J, Brieu M, Vacherand J. A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy. European Journal of Mechanics A/Solids 2006; 25(3):483-496.
    • (2006) European Journal of Mechanics A/solids , vol.25 , Issue.3 , pp. 483-496
    • Diani, J.1    Brieu, M.2    Vacherand, J.3
  • 23
    • 65649143011 scopus 로고    scopus 로고
    • A network evolution model for the anisotropic Mullins effect in carbon black filled rubbers
    • DOI: 1016/j.ijsolstr.2009.03.022
    • Dargazany R, Itskov M. A network evolution model for the anisotropic Mullins effect in carbon black filled rubbers. International Journal of Solids and Structures 2009; 46(16):2967-2977. DOI: 1016/j.ijsolstr.2009.03.022.
    • (2009) International Journal of Solids and Structures , vol.46 , Issue.16 , pp. 2967-2977
    • Dargazany, R.1    Itskov, M.2
  • 28
    • 0007080753 scopus 로고
    • Optimal spherical designs and numerical integration on the sphere
    • Neutsch W. Optimal spherical designs and numerical integration on the sphere. Journal of Computational Physics 1983; 51:313-325.
    • (1983) Journal of Computational Physics , vol.51 , pp. 313-325
    • Neutsch, W.1
  • 31
    • 0033241484 scopus 로고    scopus 로고
    • The distribution of points on the sphere and corresponding cubature formulae
    • Fliege J, Maier U. The distribution of points on the sphere and corresponding cubature formulae. IMA Journal of Numerical Analysis 1999; 19(2):317-334.
    • (1999) Ima Journal of Numerical Analysis , vol.19 , Issue.2 , pp. 317-334
    • Fliege, J.1    Maier, U.2
  • 34
  • 35
    • 84955424993 scopus 로고
    • On the number of nodes of cubature formulas on a sphere
    • Sobolev SL. On the number of nodes of cubature formulas on a sphere. Doklady Akademii Nauk SSSR 1962; 146:770-773.
    • (1962) Doklady Akademii Nauk Sssr , vol.146 , pp. 770-773
    • Sobolev, S.L.1
  • 36
    • 84968475632 scopus 로고
    • Optimal numerical integration on a sphere
    • McLaren AD. Optimal numerical integration on a sphere. Mathematics on Computation 1963; 17:361-383.
    • (1963) Mathematics On Computation , vol.17 , pp. 361-383
    • McLaren, A.D.1
  • 37
    • 0041027160 scopus 로고    scopus 로고
    • Constructing fully symmetric cubature formulae for the sphere
    • Heo S, Xu Y. Constructing fully symmetric cubature formulae for the sphere. Mathematics of Computation 2001; 70:269-279.
    • (2001) Mathematics of Computation , vol.70 , pp. 269-279
    • Heo, S.1    Xu, Y.2
  • 40
    • 0000186368 scopus 로고
    • A Padé approximant to the inverse Langevin function
    • Cohen A. A Padé approximant to the inverse Langevin function. Rheologica Acta 1991; 30(3):270-273.
    • (1991) Rheologica Acta , vol.30 , Issue.3 , pp. 270-273
    • Cohen, A.1
  • 43
    • 0034434740 scopus 로고    scopus 로고
    • A new constitutive framework for arterial wall mechanics and a comparative study of material models
    • Holzapfel GA, Gasser TC, Ogden RW. A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity 2000; 61(1-3):1-48.
    • (2000) Journal of Elasticity , vol.61 , Issue.1-3 , pp. 1-48
    • Holzapfel, G.A.1    Gasser, T.C.2    Ogden, R.W.3
  • 44
    • 0031213686 scopus 로고    scopus 로고
    • Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation
    • Delfino A, Stergiopulos N, Moore Jr JE, Meister J-J. Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. Journal of Biomechanics 1997; 30(8):777-786.
    • (1997) Journal of Biomechanics , vol.30 , Issue.8 , pp. 777-786
    • Delfino, A.1    Stergiopulos, N.2    Moore Jr, J.E.3    Meister, J.-J.4
  • 46
    • 34548441226 scopus 로고    scopus 로고
    • A polyconvex hyperelastic model for fiber-reinforced materials in application to soft tissues
    • Ehret AE, Itskov M. A polyconvex hyperelastic model for fiber-reinforced materials in application to soft tissues. Journal of Materials Science 2007; 42(21):8853-8863.
    • (2007) Journal of Materials Science , vol.42 , Issue.21 , pp. 8853-8863
    • Ehret, A.E.1    Itskov, M.2
  • 47
    • 73149111450 scopus 로고    scopus 로고
    • Integration nodes for the sphere, Available from, 20.11.2008
    • Integration nodes for the sphere. Available from: http://www.personal.soton.ac.uk/jf1w07/nodes/nodes.html [20.11.2008].
  • 49
    • 84963178774 scopus 로고
    • Further analysis of the data by Akaike's information criterion and the finite corrections
    • Sugiura N. Further analysis of the data by Akaike's information criterion and the finite corrections. Communications in Statistics A-Theory and Methods 1978; A7:13-26.
    • (1978) Communications In Statistics A-theory and Methods , vol.A7 , pp. 13-26
    • Sugiura, N.1
  • 52
    • 73149086806 scopus 로고    scopus 로고
    • Version 6.5 Documentation, ABAQUS, Inc
    • ABAQUS Version 6.5 Documentation, ABAQUS, Inc., 2004.
    • (2004) Abaqus


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