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Volumn 68, Issue 1, 2010, Pages 57-83

Fiber-reinforced hyperelastic solids: A realizable homogenization constitutive theory

Author keywords

Finite strain; Hamilton Jacobi equation; Homogenization; Instabilities; Microstructures

Indexed keywords

ANISOTROPIC FIBER; CLOSED FORM; CONSTITUTIVE THEORY; CYLINDRICAL FIBERS; FIBER CONCENTRATION; FINITE ELASTICITY; FINITE STRAIN; HAMILTON JACOBI EQUATIONS; HAMILTON-JACOBI EQUATION; HOMOGENIZATION; HOMOGENIZATION PROCEDURE; HOMOGENIZATION THEORY; HYPER ELASTIC; INSTABILITIES; LOCAL FIELDS; MACROSCOPIC DEFORMATIONS; MACROSCOPIC RESPONSE; MATRIX; MECHANICAL RESPONSE; MICROSTRUCTURAL INFORMATION; NEO-HOOKEAN SOLID; RANDOM DISTRIBUTION; SEQUENTIAL LAMINATES; SPECIAL CLASS; STRAIN LOADING; TRANSVERSELY ISOTROPIC; TWO-POINT CORRELATION FUNCTION;

EID: 77956262989     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-009-9359-y     Document Type: Article
Times cited : (46)

References (49)
  • 1
    • 0001005702 scopus 로고    scopus 로고
    • Impact of morphological orientation in determining mechanical properties in triblock copolymers
    • Honeker CC, Thomas EL (1996) Impact of morphological orientation in determining mechanical properties in triblock copolymers. Chem Mater 8: 1702-1714.
    • (1996) Chem Mater , vol.8 , pp. 1702-1714
    • Honeker, C.C.1    Thomas, E.L.2
  • 2
    • 0034500901 scopus 로고    scopus 로고
    • Perpendicular deformation of a near-single crystal triblock copolymer with a cylindrical morphology. 1. Synchroton SAXS
    • Honeker CC, Thomas EL, Albalak RJ, Hadjuk DA, Gruner SM, Capel MC (2000) Perpendicular deformation of a near-single crystal triblock copolymer with a cylindrical morphology. 1. Synchroton SAXS. Macromolecules 33: 9395-9406.
    • (2000) Macromolecules , vol.33 , pp. 9395-9406
    • Honeker, C.C.1    Thomas, E.L.2    Albalak, R.J.3    Hadjuk, D.A.4    Gruner, S.M.5    Capel, M.C.6
  • 3
    • 0031928341 scopus 로고    scopus 로고
    • Collagen organization in branching region of human brain arteries
    • Finlay HM, Whittaker P, Canham PB (1998) Collagen organization in branching region of human brain arteries. Stroke 29: 1595-1601.
    • (1998) Stroke , vol.29 , pp. 1595-1601
    • Finlay, H.M.1    Whittaker, P.2    Canham, P.B.3
  • 4
    • 0032431481 scopus 로고    scopus 로고
    • Material characterization of human medial collateral ligament
    • Quapp KM, Weiss JA (1998) Material characterization of human medial collateral ligament. J Biomech Eng 120: 757-763.
    • (1998) J Biomech Eng , vol.120 , pp. 757-763
    • Quapp, K.M.1    Weiss, J.A.2
  • 6
    • 0020718795 scopus 로고
    • Instability of a finitely deformed fiber-reinforced elastic material
    • Triantafyllidis N, Abeyaratne RC (1983) Instability of a finitely deformed fiber-reinforced elastic material. J Appl Mech 50: 149-156.
    • (1983) J Appl Mech , vol.50 , pp. 149-156
    • Triantafyllidis, N.1    Abeyaratne, R.C.2
  • 7
    • 0031366166 scopus 로고    scopus 로고
    • Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids
    • Qiu GY, Pence TJ (1997) Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids. J Elast 49: 1-30.
    • (1997) J Elast , vol.49 , pp. 1-30
    • Qiu, G.Y.1    Pence, T.J.2
  • 8
    • 6344291552 scopus 로고    scopus 로고
    • Mechanical response of fiber-reinforced incompressible nonlinear elastic solids
    • Merodio J, Ogden RW (2005) Mechanical response of fiber-reinforced incompressible nonlinear elastic solids. Int J Nonlinear Mech 40: 213-227.
    • (2005) Int J Nonlinear Mech , vol.40 , pp. 213-227
    • Merodio, J.1    Ogden, R.W.2
  • 9
    • 21844473053 scopus 로고    scopus 로고
    • A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids
    • Horgan CO, Saccomandi G (2005) A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids. J Mech Phys Solids 53: 1985-2015.
    • (2005) J Mech Phys Solids , vol.53 , pp. 1985-2015
    • Horgan, C.O.1    Saccomandi, G.2
  • 11
    • 31044453405 scopus 로고    scopus 로고
    • On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: II-application to cylindrical fibers
    • Lopez-Pamies O, Ponte Castañeda P (2006) On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: II-application to cylindrical fibers. J Mech Phys Solids 54: 831-863.
    • (2006) J Mech Phys Solids , vol.54 , pp. 831-863
    • Lopez-Pamies, O.1    Ponte Castañeda, P.2
  • 12
    • 29744447084 scopus 로고    scopus 로고
    • Neo-Hookean fiber-reinforced composites in finite elasticity
    • deBotton G, Hariton I, Socolsky EA (2006) Neo-Hookean fiber-reinforced composites in finite elasticity. J Mech Phys Solids 54: 533-559.
    • (2006) J Mech Phys Solids , vol.54 , pp. 533-559
    • Debotton, G.1    Hariton, I.2    Socolsky, E.A.3
  • 13
    • 34447529261 scopus 로고    scopus 로고
    • Homogenization estimates for fiber-reiforced elastomers with periodic microstructures
    • Brun M, Lopez-Pamies O, Ponte Castañeda P (2007) Homogenization estimates for fiber-reiforced elastomers with periodic microstructures. Int J Solids Struct 44: 5953-5979.
    • (2007) Int J Solids Struct , vol.44 , pp. 5953-5979
    • Brun, M.1    Lopez-Pamies, O.2    Ponte Castañeda, P.3
  • 14
    • 58149185089 scopus 로고    scopus 로고
    • A general hyperelastic model for incompressible fiber-reinforced elastomers
    • Agoras M, Lopez-Pamies O, Ponte Castañeda P (2009) A general hyperelastic model for incompressible fiber-reinforced elastomers. J Mech Phys Solids 57: 268-286.
    • (2009) J Mech Phys Solids , vol.57 , pp. 268-286
    • Agoras, M.1    Lopez-Pamies, O.2    Ponte Castañeda, P.3
  • 15
    • 44649137332 scopus 로고    scopus 로고
    • Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates
    • Idiart MI (2008) Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates. J Mech Phys Solids 56: 2599-2617.
    • (2008) J Mech Phys Solids , vol.56 , pp. 2599-2617
    • Idiart, M.I.1
  • 16
    • 16344369729 scopus 로고    scopus 로고
    • Transversely isotropic sequentially laminated composites in finite elasticity
    • deBotton G (2005) Transversely isotropic sequentially laminated composites in finite elasticity. J Mech Phys Solids 53: 1334-1361.
    • (2005) J Mech Phys Solids , vol.53 , pp. 1334-1361
    • Debotton, G.1
  • 17
    • 77956268360 scopus 로고    scopus 로고
    • Lopez-Pamies O (2006) On the effective behavior, microstructure evolution, and macroscopic stability of elastomeric composites. Ph. D. Dissertation, University of Pennsylvania, USA.
  • 18
    • 0002767124 scopus 로고
    • Elasticity theory of composites
    • H. G. Hopkins and M. J. Sewell (Eds.), Oxford: Pergamon Press
    • Willis JR (1982) Elasticity theory of composites. In: Hopkins HG, Sewell MJ (eds) Mechanics of solids, The Rodney Hill 60th anniversary volume. Pergamon Press, Oxford, pp 653-686.
    • (1982) Mechanics of Solids, The Rodney Hill 60th Anniversary Volume , pp. 653-686
    • Willis, J.R.1
  • 19
    • 0001155575 scopus 로고
    • On constitutive macrovariables for heterogeneous solids at finite strain
    • Hill R (1972) On constitutive macrovariables for heterogeneous solids at finite strain. Proc R Soc Lond A 326: 131-147.
    • (1972) Proc R Soc Lond A , vol.326 , pp. 131-147
    • Hill, R.1
  • 20
    • 21144480320 scopus 로고
    • Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity
    • Geymonat G, Müller S, Triantafyllidis N (1993) Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity. Arch Ration Mech Anal 122: 231-290.
    • (1993) Arch Ration Mech Anal , vol.122 , pp. 231-290
    • Geymonat, G.1    Müller, S.2    Triantafyllidis, N.3
  • 21
    • 33745028217 scopus 로고    scopus 로고
    • Failure surfaces for finitely strained two-phase periodic solids under general in-plane loading
    • Triantafyllidis N, Nestorovic MD, Schaard MW (2006) Failure surfaces for finitely strained two-phase periodic solids under general in-plane loading. J Appl Mech 73: 505-516.
    • (2006) J Appl Mech , vol.73 , pp. 505-516
    • Triantafyllidis, N.1    Nestorovic, M.D.2    Schaard, M.W.3
  • 23
    • 77956264590 scopus 로고    scopus 로고
    • Michel JC, Lopez-Pamies O, Ponte Castañeda P, Triantafyllidis N (2010) Microscopic and macroscopic instabilities in finitely strained particle-reinforced elastomers (submitted).
  • 24
    • 62649134212 scopus 로고    scopus 로고
    • Microstructure evolution in hyperelastic laminates and implications for overall behavior and macroscopic stability
    • Lopez-Pamies O, Ponte Castañeda P (2009) Microstructure evolution in hyperelastic laminates and implications for overall behavior and macroscopic stability. Mech Mater 41: 364-374.
    • (2009) Mech Mater , vol.41 , pp. 364-374
    • Lopez-Pamies, O.1    Ponte Castañeda, P.2
  • 25
    • 0021976554 scopus 로고
    • Large isotropic elastic deformation of composites and porous media
    • Hashin Z (1985) Large isotropic elastic deformation of composites and porous media. Int J Solids Struct 21: 711-720.
    • (1985) Int J Solids Struct , vol.21 , pp. 711-720
    • Hashin, Z.1
  • 26
    • 84980703555 scopus 로고    scopus 로고
    • Bruggerman DAG (1935) Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizittskonstanten und Leitfhigkeiten der Mischkrper aus isotropen Substanzen (German) [Calculation of various physical constants in heterogeneous substances. I. Dielectric constants and conductivity of composites from isotropic substances]. Ann Phys 416: 636-664.
  • 27
    • 0004025336 scopus 로고    scopus 로고
    • Cambridge, UK: Cambridge University Press
    • Milton G (2002) The theory of composites. Cambridge University Press, Cambridge, UK.
    • (2002) The Theory of Composites
    • Milton, G.1
  • 28
    • 0021504978 scopus 로고
    • A self-consistent analysis of the stiffening effect of rigid inclusions on a power-law material
    • Duva JM (1984) A self-consistent analysis of the stiffening effect of rigid inclusions on a power-law material. ASME J Eng Mater Technol 106: 317-321.
    • (1984) ASME J Eng Mater Technol , vol.106 , pp. 317-321
    • Duva, J.M.1
  • 29
    • 75249097490 scopus 로고    scopus 로고
    • An exact result for the macroscopic response of particle-reinforced Neo-Hookean solids
    • Lopez-Pamies O (2010) An exact result for the macroscopic response of particle-reinforced Neo-Hookean solids. J Appl Mech 77: 021016-10210165.
    • (2010) J Appl Mech , vol.77 , pp. 021016-10210165
    • Lopez-Pamies, O.1
  • 30
    • 0000929676 scopus 로고
    • The determination of the elastic field of an ellipsoidal inclusion and related problems
    • Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc R Soc Lond A 241: 376-396.
    • (1957) Proc R Soc Lond A , vol.241 , pp. 376-396
    • Eshelby, J.D.1
  • 31
    • 31044441045 scopus 로고    scopus 로고
    • On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformation: I-theory
    • Lopez-Pamies O, Ponte Castañeda P (2006) On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformation: I-theory. J Mech Phys Solids 54: 807-830.
    • (2006) J Mech Phys Solids , vol.54 , pp. 807-830
    • Lopez-Pamies, O.1    Ponte Castañeda, P.2
  • 32
    • 58549115677 scopus 로고    scopus 로고
    • Onset of cavitation in compressible, isotropic, hyperelastic solids
    • Lopez-Pamies O (2009) Onset of cavitation in compressible, isotropic, hyperelastic solids. J Elast 94: 115-145.
    • (2009) J Elast , vol.94 , pp. 115-145
    • Lopez-Pamies, O.1
  • 33
    • 84886586721 scopus 로고
    • On the comparison between microscopic and macroscopic instability mechanisms in a class of fiber-reinforced composites
    • Triantafyllidis N, Maker BN (1985) On the comparison between microscopic and macroscopic instability mechanisms in a class of fiber-reinforced composites. J Appl Mech 52: 794-800.
    • (1985) J Appl Mech , vol.52 , pp. 794-800
    • Triantafyllidis, N.1    Maker, B.N.2
  • 34
    • 1442359332 scopus 로고    scopus 로고
    • Onset of failure in finitely strained layered composites subjected to combined normal and shear loading
    • Nesterovic N, Triantafyllidis N (2004) Onset of failure in finitely strained layered composites subjected to combined normal and shear loading. J Mech Phys Solids 52: 941-974.
    • (2004) J Mech Phys Solids , vol.52 , pp. 941-974
    • Nesterovic, N.1    Triantafyllidis, N.2
  • 35
    • 39049146499 scopus 로고    scopus 로고
    • Optimization of structural topology in the high-porosity regime
    • Bourdin B, Kohn R (2008) Optimization of structural topology in the high-porosity regime. J Mech Phys Solids 56: 1043-1064.
    • (2008) J Mech Phys Solids , vol.56 , pp. 1043-1064
    • Bourdin, B.1    Kohn, R.2
  • 36
    • 0017502751 scopus 로고
    • Bounds and self-consistent estimates for the overall moduli of anisotropic composites
    • Willis JR (1977) Bounds and self-consistent estimates for the overall moduli of anisotropic composites. J Mech Phys Solids 25: 185-202.
    • (1977) J Mech Phys Solids , vol.25 , pp. 185-202
    • Willis, J.R.1
  • 38
    • 0029541225 scopus 로고
    • The effect of spatial distribution on the effective behavior of composite materials and cracked media
    • Ponte Castañeda P, Willis JR (1995) The effect of spatial distribution on the effective behavior of composite materials and cracked media. J Mech Phys Solids 43: 1919-1951.
    • (1995) J Mech Phys Solids , vol.43 , pp. 1919-1951
    • Ponte Castañeda, P.1    Willis, J.R.2
  • 39
    • 0017442448 scopus 로고
    • A study of the differential scheme for composite materials
    • McLaughlin R (1977) A study of the differential scheme for composite materials. Int J Eng Sci 15: 237-244.
    • (1977) Int J Eng Sci , vol.15 , pp. 237-244
    • McLaughlin, R.1
  • 40
    • 0017927099 scopus 로고    scopus 로고
    • Ogden R (1978) Extremum principles in non-linear elasticity and theirapplication to composites-I Theory Int J Solids Struct. 14: 265-282.
  • 41
    • 33645659764 scopus 로고    scopus 로고
    • Exact results for the homogenization of elastic fiber-reinforced solids at finite strain
    • He QC, Le Quang H, Feng ZQ (2006) Exact results for the homogenization of elastic fiber-reinforced solids at finite strain. J Elast 83: 153-177.
    • (2006) J Elast , vol.83 , pp. 153-177
    • He, Q.C.1    Le Quang, H.2    Feng, Z.Q.3
  • 42
    • 77956266140 scopus 로고    scopus 로고
    • Idiart MI, Lopez-Pamies O (2010) Two-phase hyperelastic composites: a realizable homogenization constitutive theory (in preparation).
  • 44
    • 0041312550 scopus 로고    scopus 로고
    • Instabilities and loss of ellipticity in fiber-reinforced nonlinearly elastic solids under plane deformation
    • Merodio J, Ogden RW (2003) Instabilities and loss of ellipticity in fiber-reinforced nonlinearly elastic solids under plane deformation. Int J Solids Struct 40: 4707-4727.
    • (2003) Int J Solids Struct , vol.40 , pp. 4707-4727
    • Merodio, J.1    Ogden, R.W.2
  • 45
    • 0026839894 scopus 로고
    • Characterization of bounds and perturbation series for transversely isotropic, incompressible elastic composites
    • Lipton R (1992) Characterization of bounds and perturbation series for transversely isotropic, incompressible elastic composites. J Elast 27: 193-225.
    • (1992) J Elast , vol.27 , pp. 193-225
    • Lipton, R.1
  • 47
    • 68049111468 scopus 로고    scopus 로고
    • Moraleda J, Segurado J, Llorca J (2009) Finite deformation of incompressible fiber-reinforced elastomers: a computational micromechanics approach. J Mech Phys Solids. doi: 10. 1016/j. jmps. 2009. 05. 007.
  • 49
    • 0001043806 scopus 로고
    • Large elastic deformations of homogeneous anisotropic materials
    • Ericksen JL, Rivlin RS (1954) Large elastic deformations of homogeneous anisotropic materials. J Ration Mech Anal 3: 281-301.
    • (1954) J Ration Mech Anal , vol.3 , pp. 281-301
    • Ericksen, J.L.1    Rivlin, R.S.2


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