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Volumn 45, Issue 7, 1997, Pages 1223-1252

Thermal expansion of isotropic multiphase composites and polycrystals

Author keywords

A. Thermomechanical processes; B. Inhomogeneous material; B. Polycrystalline material; B. Thermal expansion; C. Variational calculus

Indexed keywords

ANISOTROPY; COMPOSITE MATERIALS; THERMAL EXPANSION; THERMOMECHANICAL TREATMENT; VARIATIONAL TECHNIQUES;

EID: 0031189075     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(96)00129-9     Document Type: Article
Times cited : (79)

References (50)
  • 1
    • 0000761445 scopus 로고
    • Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials
    • Allaire, G. and Kohn, R., (1993) Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials. Q. Appl. Math. 51, 643-674.
    • (1993) Q. Appl. Math. , vol.51 , pp. 643-674
    • Allaire, G.1    Kohn, R.2
  • 2
    • 0000350984 scopus 로고
    • Optimal bounds on the effective bulk modulus of polycrystals
    • Avellaneda, M. and Milton, G. W. (1989) Optimal bounds on the effective bulk modulus of polycrystals. SIAM J. Appl. Math. 49, 824-837.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 824-837
    • Avellaneda, M.1    Milton, G.W.2
  • 3
    • 0030190272 scopus 로고    scopus 로고
    • On the effective conductivity of polycrystals and a three-dimensional phase-interchange inequality
    • Avellaneda, M., Cherkaev, A. V., Gibiansky, L. V., Milton, G. W. and Rudelson, M. (1996) On the effective conductivity of polycrystals and a three-dimensional phase-interchange inequality. J. Mech. Phys. Solids 44(7), 1179-1218.
    • (1996) J. Mech. Phys. Solids , vol.44 , Issue.7 , pp. 1179-1218
    • Avellaneda, M.1    Cherkaev, A.V.2    Gibiansky, L.V.3    Milton, G.W.4    Rudelson, M.5
  • 4
    • 0043125160 scopus 로고    scopus 로고
    • Thermal expansion of polycrystalline aggregates consisting of elongated crystals and containing cylindrical pores or inclusions
    • Benveniste, Y. (1996) Thermal expansion of polycrystalline aggregates consisting of elongated crystals and containing cylindrical pores or inclusions. J. Mech. Phys. Solids 44(1), 137-153.
    • (1996) J. Mech. Phys. Solids , vol.44 , Issue.1 , pp. 137-153
    • Benveniste, Y.1
  • 5
    • 0026359387 scopus 로고
    • Exact results for generalized Gassman's equations in composite porous media with two constituents
    • Berryman, J. and Milton, G. W. (1991) Exact results for generalized Gassman's equations in composite porous media with two constituents. Geophysics 56, 1950-1960.
    • (1991) Geophysics , vol.56 , pp. 1950-1960
    • Berryman, J.1    Milton, G.W.2
  • 6
    • 0031240687 scopus 로고    scopus 로고
    • Elastic energy minimization and the recoverable strains of polycrystalline shape-memory materials
    • in press
    • Bhattacharya, K. and Kohn, R. V. (1997) Elastic energy minimization and the recoverable strains of polycrystalline shape-memory materials. Arch. Rat. Mech. Anal., in press.
    • (1997) Arch. Rat. Mech. Anal.
    • Bhattacharya, K.1    Kohn, R.V.2
  • 7
    • 36849124387 scopus 로고
    • Thermoelasticity and irreversible thermodynamics
    • Biot, M. A. (1956) Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27, 240-253.
    • (1956) J. Appl. Phys. , vol.27 , pp. 240-253
    • Biot, M.A.1
  • 8
    • 84971149887 scopus 로고
    • The exact coupled bounds for effective tensors of electrical and magnetic properties of two-component two-dimensional composites
    • Cherkaev, A. V. and Gibiansky, L. V. (1992) The exact coupled bounds for effective tensors of electrical and magnetic properties of two-component two-dimensional composites. Proc. R. Soc. Edinburgh 122A, 93-125.
    • (1992) Proc. R. Soc. Edinburgh , vol.122 A , pp. 93-125
    • Cherkaev, A.V.1    Gibiansky, L.V.2
  • 9
    • 0027590093 scopus 로고
    • Coupled estimates for the bulk and shear moduli of a two-dimensional isotropic elastic composite
    • Cherkaev, A. V. and Gibiansky, L. V. (1993) Coupled estimates for the bulk and shear moduli of a two-dimensional isotropic elastic composite. J. Mech. Phys. Solids 41, 937-980.
    • (1993) J. Mech. Phys. Solids , vol.41 , pp. 937-980
    • Cherkaev, A.V.1    Gibiansky, L.V.2
  • 11
    • 0000150685 scopus 로고
    • Shrinkage and thermal expansion of a two-phase material
    • Cribb, J. L. (1968) Shrinkage and thermal expansion of a two-phase material. Nature 220, 576-577.
    • (1968) Nature , vol.220 , pp. 576-577
    • Cribb, J.L.1
  • 12
    • 0003197193 scopus 로고
    • Weak continuity and weak lower semicontinuity of non-linear functionals
    • Springer-Verlag, Berlin
    • Dacorogna, B. (1982) Weak Continuity and Weak Lower Semicontinuity of Non-linear Functionals. Lecture Notes in Math. 922. Springer-Verlag, Berlin.
    • (1982) Lecture Notes in Math. , vol.922
    • Dacorogna, B.1
  • 13
    • 0022861560 scopus 로고
    • Thermal expansion of elastic plastic composite materials
    • Dvorak, G. . (1986) Thermal expansion of elastic plastic composite materials. ASME J. Appl. Mech. 53, 737-743.
    • (1986) ASME J. Appl. Mech. , vol.53 , pp. 737-743
    • Dvorak, G.1
  • 14
    • 0024681887 scopus 로고
    • Thermal expansion of three-phase composite materials
    • Dvorak, G. J. and Chen, T. (1989) Thermal expansion of three-phase composite materials. ASME J. Appl. Mech. 56, 418-422.
    • (1989) ASME J. Appl. Mech. , vol.56 , pp. 418-422
    • Dvorak, G.J.1    Chen, T.2
  • 15
    • 0022862030 scopus 로고
    • Homogenization and optimal bounds in linear elasticity
    • Francfort, G. A. and Murat, F. (1986) Homogenization and optimal bounds in linear elasticity. Arch. Rat. Mech. Anal. 94, 307-334.
    • (1986) Arch. Rat. Mech. Anal. , vol.94 , pp. 307-334
    • Francfort, G.A.1    Murat, F.2
  • 16
    • 0040794563 scopus 로고
    • Design of composite plates of extremal rigidity
    • Ioffe Physico-Technical Institute, preprint #914, Leningrad. English translation in: A. V. Cherkaev and R. Kohn (eds) Birkhausen, New York
    • Gibiansky, L. V. and Cherkaev, A. V. (1984) Design of composite plates of extremal rigidity. Ioffe Physico-Technical Institute, preprint #914, Leningrad. English translation in: A. V. Cherkaev and R. Kohn (eds) (1997) Topics in the Mathematical Modeling of Composite Materials. Birkhausen, New York.
    • (1984) Topics in the Mathematical Modeling of Composite Materials
    • Gibiansky, L.V.1    Cherkaev, A.V.2
  • 17
    • 0037786409 scopus 로고
    • Microstructures of composites of extremal rigidity and exact estimates of provided energy density
    • Ioffe Physico-Technical Institute, preprint #1115, Leningrad. English translation in: A. V. Cherkaev and R. Kohn (eds) Birkhausen, New York
    • Gibiansky, L. V. and Cherkaev, A. V. (1987) Microstructures of composites of extremal rigidity and exact estimates of provided energy density. Ioffe Physico-Technical Institute, preprint #1115, Leningrad. English translation in: A. V. Cherkaev and R. Kohn (eds) (1997) Topics in the Mathematical Modeling of Composite Materials. Birkhausen, New York.
    • (1987) Topics in the Mathematical Modeling of Composite Materials
    • Gibiansky, L.V.1    Cherkaev, A.V.2
  • 18
    • 0001406167 scopus 로고
    • On the effective viscoelastic moduli of two-phase media: I. rigorous bounds on the complex bulk modulus
    • Gibiansky, L. V. and Milton, G. W. (1993) On the effective viscoelastic moduli of two-phase media: I. Rigorous bounds on the complex bulk modulus. Proc. R. Soc. Lond. A440, 163-188.
    • (1993) Proc. R. Soc. Lond. , vol.A440 , pp. 163-188
    • Gibiansky, L.V.1    Milton, G.W.2
  • 19
    • 0008621742 scopus 로고    scopus 로고
    • Rigorous link between the conductivity and elastic moduli of fiber reinforced materials
    • Gibiansky, L. V. and Torquato, S. (1995a) Rigorous link between the conductivity and elastic moduli of fiber reinforced materials. Phil. Trans. R. Soc. Lond. A452, 253-283.
    • (1995) Phil. Trans. R. Soc. Lond. , vol.A452 , pp. 253-283
    • Gibiansky, L.V.1    Torquato, S.2
  • 20
    • 0001130959 scopus 로고
    • Geometrical-parameter bounds on the effective moduli of composites
    • Gibiansky, L. V. and Torquato, S. (1995b) Geometrical-parameter bounds on the effective moduli of composites. J. Mech. Phys. Solids 43(10), 1587-1613.
    • (1995) J. Mech. Phys. Solids , vol.43 , Issue.10 , pp. 1587-1613
    • Gibiansky, L.V.1    Torquato, S.2
  • 21
    • 0008621742 scopus 로고    scopus 로고
    • Connection between the conductivity and bulk modulus of isotropic composite materials
    • Gibiansky, L. V. and Torquato, S. (1996a) Connection between the conductivity and bulk modulus of isotropic composite materials. Proc. R. Soc. Lond. A353, 243-278.
    • (1996) Proc. R. Soc. Lond. , vol.A353 , pp. 243-278
    • Gibiansky, L.V.1    Torquato, S.2
  • 22
    • 0041621259 scopus 로고    scopus 로고
    • Phase-interchange relations for the elastic moduli of two-phase composites
    • Gibiansky, L. V. and Torquato, S. (1996b) Phase-interchange relations for the elastic moduli of two-phase composites. Int. J. Engng Sci. 34(7), 739-760.
    • (1996) Int. J. Engng Sci. , vol.34 , Issue.7 , pp. 739-760
    • Gibiansky, L.V.1    Torquato, S.2
  • 23
    • 0021197598 scopus 로고
    • Thermal expansion of polycrystalline aggregates: I. Exact analysis
    • Hashin, Z., (1984) Thermal expansion of polycrystalline aggregates: I. Exact analysis. J. Mech. Phys. Solids 32(2), 149-157.
    • (1984) J. Mech. Phys. Solids , vol.32 , Issue.2 , pp. 149-157
    • Hashin, Z.1
  • 24
    • 11644258018 scopus 로고
    • A variational approach to the theory of the elastic behavior of polycrystals
    • Hashin, Z. and Shtrikman, S. (1962) A variational approach to the theory of the elastic behavior of polycrystals, J. Mech. Phys. Solids 10, 343-352.
    • (1962) J. Mech. Phys. Solids , vol.10 , pp. 343-352
    • Hashin, Z.1    Shtrikman, S.2
  • 25
    • 0007544668 scopus 로고
    • A variational approach to the theory of the elastic behavior of multiphase materials
    • Hashin, Z. and Shtrikman, S. (1963) A variational approach to the theory of the elastic behavior of multiphase materials. J. Mech. Phys. Solids 11, 127-140.
    • (1963) J. Mech. Phys. Solids , vol.11 , pp. 127-140
    • Hashin, Z.1    Shtrikman, S.2
  • 26
    • 33144479510 scopus 로고
    • The elastic behavior of a crystalline aggregate
    • Hill, R. (1952) The elastic behavior of a crystalline aggregate. Proc. Phys. Soc. Lond. A65, 349-354.
    • (1952) Proc. Phys. Soc. Lond. , vol.A65 , pp. 349-354
    • Hill, R.1
  • 27
    • 84990623154 scopus 로고
    • Optimal design and relaxation of variational problems I, II, III
    • Kohn, R. V. and Strang, G. (1986) Optimal design and relaxation of variational problems I, II, III. Comm. Pure Appl. Math. 39, 113-137, 139-182, 353-377.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 113-137
    • Kohn, R.V.1    Strang, G.2
  • 28
    • 0003259901 scopus 로고
    • On the coefficients of thermal expansion of heterogeneous materials
    • in Russian
    • Levin, V. M. (1967) On the coefficients of thermal expansion of heterogeneous materials. Mekhanika Tverdogo Tela 2, 88-94 (in Russian).
    • (1967) Mekhanika Tverdogo Tela , vol.2 , pp. 88-94
    • Levin, V.M.1
  • 29
    • 84971195680 scopus 로고
    • Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion
    • Lurie, K. A. and Cherkaev, A. V. (1984) Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion. Proc. R. Soc. Edinburgh A99, 71-87.
    • (1984) Proc. R. Soc. Edinburgh , vol.A99 , pp. 71-87
    • Lurie, K.A.1    Cherkaev, A.V.2
  • 30
    • 84974267674 scopus 로고
    • Exact estimates of the conductivity of a binary mixture of isotropic materials
    • Lurie, K. A. and Cherkaev, A. V. (1986a) Exact estimates of the conductivity of a binary mixture of isotropic materials. Proc. R. Soc. Edinburgh A104, 21-38.
    • (1986) Proc. R. Soc. Edinburgh , vol.A104 , pp. 21-38
    • Lurie, K.A.1    Cherkaev, A.V.2
  • 31
    • 0002338788 scopus 로고
    • The effective characteristics of composite materials and optimal design of constructions
    • Poland
    • Lurie, K. A. and Cherkaev, A. V. (1986b) The effective characteristics of composite materials and optimal design of constructions. Advances in Mechanics (Poland) 9, 3-81.
    • (1986) Advances in Mechanics , vol.9 , pp. 3-81
    • Lurie, K.A.1    Cherkaev, A.V.2
  • 32
    • 0020169555 scopus 로고    scopus 로고
    • Regularization of optimal problems of design of bars and plates and solving the contradiction in a system of necessary conditions of optimality
    • Lurie, K. A., Cherkaev, A. V. and Fedorov, A. V. (1982) Regularization of optimal problems of design of bars and plates and solving the contradiction in a system of necessary conditions of optimality. J. Opt. Th. Appl. 37(4), 499-522 (part 1), 523-542 (part 2).
    • (1982) J. Opt. Th. Appl. , vol.37 , Issue.4 PART 1 , pp. 499-522
    • Lurie, K.A.1    Cherkaev, A.V.2    Fedorov, A.V.3
  • 33
    • 0020169555 scopus 로고    scopus 로고
    • Lurie, K. A., Cherkaev, A. V. and Fedorov, A. V. (1982) Regularization of optimal problems of design of bars and plates and solving the contradiction in a system of necessary conditions of optimality. J. Opt. Th. Appl. 37(4), 499-522 (part 1), 523-542 (part 2).
    • J. Opt. Th. Appl. , Issue.2 PART , pp. 523-542
  • 34
    • 0041621233 scopus 로고    scopus 로고
    • MAPLE V (1981) Release 2, Princeton University, Copyright (©) 1981-1992 by the University of Waterloo
    • MAPLE V (1981) Release 2, Princeton University, Copyright (©) 1981-1992 by the University of Waterloo.
  • 35
    • 0019624607 scopus 로고
    • Concerning bounds on the transport and mechanical properties of multicomponent composite materials
    • Milton, G. W. (1981) Concerning bounds on the transport and mechanical properties of multicomponent composite materials. Appl. Phys. A26, 125.
    • (1981) Appl. Phys. , vol.A26 , pp. 125
    • Milton, G.W.1
  • 36
    • 84990557371 scopus 로고
    • On characterizing the set of possible effective tensors of composites : The variational method and the translation method
    • Milton, G. W. (1990a) On characterizing the set of possible effective tensors of composites : the variational method and the translation method, Comm. Pure Appl. Math. XLIII, 63-125.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 63-125
    • Milton, G.W.1
  • 37
    • 0041621235 scopus 로고
    • A brief review of the translation method for bounding effective elastic tensors of composites
    • ed. G. A. Maugin, Wiley, New York
    • Milton, G. W. (1990b) A brief review of the translation method for bounding effective elastic tensors of composites. In Continuum Models and Discrete Systems, ed. G. A. Maugin, Vol. 1, pp. 60-74. Wiley, New York.
    • (1990) Continuum Models and Discrete Systems , vol.1 , pp. 60-74
    • Milton, G.W.1
  • 39
    • 0000274856 scopus 로고
    • On the correspondence between poroelasticity and thermoelasticity
    • Norris, A. (1992) On the correspondence between poroelasticity and thermoelasticity. J. Appl. Phys. 71, 1138-1141.
    • (1992) J. Appl. Phys. , vol.71 , pp. 1138-1141
    • Norris, A.1
  • 40
    • 0016950848 scopus 로고
    • Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents
    • Rice, J. R. and Cleary, M. P. (1976) Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Rev. Geophys. Space Phys. 14, 227-241.
    • (1976) Rev. Geophys. Space Phys. , vol.14 , pp. 227-241
    • Rice, J.R.1    Cleary, M.P.2
  • 41
    • 0014707594 scopus 로고
    • Thermoelastic energy functions and minimum energy principles for composite materials
    • Rosen, B. W. (1970) Thermoelastic energy functions and minimum energy principles for composite materials. Int. J. Engng Sci. 8(1), 5-18.
    • (1970) Int. J. Engng Sci. , vol.8 , Issue.1 , pp. 5-18
    • Rosen, B.W.1
  • 42
    • 0014735918 scopus 로고
    • Effective thermal expansion coefficients and specific heats of composite materials
    • Rosen, B. W. and Hashin, Z. (1970) Effective thermal expansion coefficients and specific heats of composite materials. Int. J. Engng Sci. 8, 157-173.
    • (1970) Int. J. Engng Sci. , vol.8 , pp. 157-173
    • Rosen, B.W.1    Hashin, Z.2
  • 43
    • 84964172898 scopus 로고
    • Thermal expansion coefficients of composite materials based on energy principles
    • Schapery, R. A. (1968) Thermal expansion coefficients of composite materials based on energy principles. J. Comp. Mat. 2, 380-404.
    • (1968) J. Comp. Mat. , vol.2 , pp. 380-404
    • Schapery, R.A.1
  • 44
    • 0023111602 scopus 로고
    • Thermal expansion of polycrystalline aggregates with texture
    • Schulgasser, K. (1987) Thermal expansion of polycrystalline aggregates with texture. J. Mech. Phys. Solids 35(1), 35-42.
    • (1987) J. Mech. Phys. Solids , vol.35 , Issue.1 , pp. 35-42
    • Schulgasser, K.1
  • 45
    • 0041621231 scopus 로고
    • Thermal expansion of polycrystals
    • Schulgasser, K. (1989a) Thermal expansion of polycrystals. J. Mater. Sci. Lett. 8, 228-229.
    • (1989) J. Mater. Sci. Lett. , vol.8 , pp. 228-229
    • Schulgasser, K.1
  • 46
    • 0024621660 scopus 로고
    • The relationship between stiffness and thermal expansion of carbon fibers
    • Schulgasser, K. (1989b) The relationship between stiffness and thermal expansion of carbon fibers. Mater. Sci. Engng A-110, L35-L37.
    • (1989) Mater. Sci. Engng , vol.A-110
    • Schulgasser, K.1
  • 47
    • 0001424622 scopus 로고    scopus 로고
    • Design of materials with extreme thermal expansion using three-phase topology optimization method
    • Sigmund, O. and Torquato, S. (1996) Design of materials with extreme thermal expansion using three-phase topology optimization method. Appl. Phys. Lett. 69, 3203-3205.
    • (1996) Appl. Phys. Lett. , vol.69 , pp. 3203-3205
    • Sigmund, O.1    Torquato, S.2
  • 48
    • 0031169474 scopus 로고    scopus 로고
    • Design of materials with extreme thermal expansion using three-phase topology optimization method
    • Sigmund, O. and Torquato, S. (1997) Design of materials with extreme thermal expansion using three-phase topology optimization method. J. Phys. Mech. Solids 45(6), 1037-1067.
    • (1997) J. Phys. Mech. Solids , vol.45 , Issue.6 , pp. 1037-1067
    • Sigmund, O.1    Torquato, S.2
  • 49
    • 0001156303 scopus 로고
    • Estimation de coefficients homogeneises
    • Computing Methods in Applied Sciences and Engineering, Springer-Verlag, Berlin
    • Tartar, L. (1978) Estimation de coefficients homogeneises. In Computing Methods in Applied Sciences and Engineering, Lecture Notes in Math. 704, 364-373. Springer-Verlag, Berlin.
    • (1978) Lecture Notes in Math. , vol.704 , pp. 364-373
    • Tartar, L.1
  • 50
    • 0001357333 scopus 로고
    • Estimations fines des coefficients homogeneises
    • ed. P. Kree, Pitman Research Notes in Math. Wiley, New York
    • Tartar, L. (1985) Estimations fines des coefficients homogeneises. In Ennio de Giorgi Colloquium, ed. P. Kree, Pitman Research Notes in Math. pp. 125, 168-187. Wiley, New York.
    • (1985) Ennio de Giorgi Colloquium , pp. 125
    • Tartar, L.1


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