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Volumn 44, Issue 7, 1996, Pages 1179-1218

A complete characterization of the possible bulk and shear moduli of planar polycrystals

Author keywords

[No Author keywords available]

Indexed keywords

CHARACTERIZATION; CRYSTAL MICROSTRUCTURE; CRYSTAL SYMMETRY; ELASTICITY; OPTIMIZATION; POLYCRYSTALS;

EID: 0030190272     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/0022-5096(96)00018-X     Document Type: Article
Times cited : (38)

References (40)
  • 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
  • 4
    • 0001582295 scopus 로고
    • On the effective conductivity of polycrystals and a three-dimensional phase-interchange inequality
    • Avellaneda, M., Cherkaev, A. V., Lurie, K. A. and Milton, G. W. (1988) On the effective conductivity of polycrystals and a three-dimensional phase-interchange inequality. J. Appl. Phys. 63, 4989-5003.
    • (1988) J. Appl. Phys. , vol.63 , pp. 4989-5003
    • Avellaneda, M.1    Cherkaev, A.V.2    Lurie, K.A.3    Milton, G.W.4
  • 5
    • 0028768652 scopus 로고
    • Exact connections between polycrystals and crystal properties in two-dimensional polycrystalline aggregates
    • Benveniste, Y. (1994) Exact connections between polycrystals and crystal properties in two-dimensional polycrystalline aggregates. Proc. Roy. Soc. Lond. A 447, 1-22.
    • (1994) Proc. Roy. Soc. Lond. A , vol.447 , pp. 1-22
    • Benveniste, Y.1
  • 6
    • 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
  • 8
    • 0003197193 scopus 로고
    • Weak continuity and weak lower semicontinuity of non-linear functionals
    • Springer-Verlag
    • Dacorogna, B. (1982) Weak continuity and weak lower semicontinuity of non-linear functionals. Lecture Notes in Mathematics 922, Springer-Verlag.
    • (1982) Lecture Notes in Mathematics , vol.922
    • Dacorogna, B.1
  • 9
    • 0001363511 scopus 로고
    • Conductivity of a two-dimensional two-phase system
    • Dykhne, A. M. (1970) Conductivity of a two-dimensional two-phase system. Zh. Eksp. Teor. Fiz. 59, 110-115 [Soviet Physics JETP 32 (1971), 63-65].
    • (1970) Zh. Eksp. Teor. Fiz. , vol.59 , pp. 110-115
    • Dykhne, A.M.1
  • 10
    • 0007265745 scopus 로고
    • Dykhne, A. M. (1970) Conductivity of a two-dimensional two-phase system. Zh. Eksp. Teor. Fiz. 59, 110-115 [Soviet Physics JETP 32 (1971), 63-65].
    • (1971) Soviet Physics JETP , vol.32 , pp. 63-65
  • 11
    • 84990666070 scopus 로고
    • Sets of conductivity and elasticity tensors stable under laminations
    • Francfort, G. A. and Milton, G. W. (1994) Sets of conductivity and elasticity tensors stable under laminations. Comm. Pure Appl. Math. XLVII, 257-279.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 257-279
    • Francfort, G.A.1    Milton, G.W.2
  • 12
    • 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, 149-151.
    • (1984) J. Mech. Phys. Solids , vol.32 , pp. 149-151
    • Hashin, Z.1
  • 13
    • 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
  • 14
    • 0000458239 scopus 로고
    • Effective conductivity of aggregates of anisotropic grains
    • Helsing, J. and Helte, A. (1991) Effective conductivity of aggregates of anisotropic grains. J. Appl. Phys. 69, 3583.
    • (1991) J. Appl. Phys. , vol.69 , pp. 3583
    • Helsing, J.1    Helte, A.2
  • 15
    • 85143526052 scopus 로고
    • The elasticity of an isotropic aggregate of anisotropic cubic crystals
    • Hershey, A. V. (1954) The elasticity of an isotropic aggregate of anisotropic cubic crystals. J. Appl. Mech. 21, 236-240.
    • (1954) J. Appl. Mech. , vol.21 , pp. 236-240
    • Hershey, A.V.1
  • 16
    • 33144479510 scopus 로고
    • The elastic behavior of a crystalline aggregate
    • Hill, R. (1952) The elastic behavior of a crystalline aggregate. Proc. Phys. Soc. London A 65, 349-354.
    • (1952) Proc. Phys. Soc. London A , vol.65 , pp. 349-354
    • Hill, R.1
  • 17
    • 6544226089 scopus 로고
    • Elastic properties of reinforced solids: Some theoretical principles
    • Hill, R. (1963) Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11, 357-372.
    • (1963) J. Mech. Phys. Solids , vol.11 , pp. 357-372
    • Hill, R.1
  • 18
    • 0345285907 scopus 로고
    • Theory of mechanical properties of fibre-strengthened materials - I. Elastic behavior
    • Hill, R. (1964) Theory of mechanical properties of fibre-strengthened materials - I. Elastic behavior. J. Mech. Phys. Solids 12, 199-212.
    • (1964) J. Mech. Phys. Solids , vol.12 , pp. 199-212
    • Hill, R.1
  • 19
    • 84984305124 scopus 로고
    • Calculation of elastic moduli of polycrystalline aggregates with texture
    • Kneer, G. (1965) Calculation of elastic moduli of polycrystalline aggregates with texture. Phys. Stat. Solidi 9, 825-838.
    • (1965) Phys. Stat. Solidi , vol.9 , pp. 825-838
    • Kneer, G.1
  • 20
    • 0007200514 scopus 로고
    • G-closure of some particular sets of admissible material characteristics for the problem of bending of thin plates
    • Lurie, K. A. and Cherkaev, A. V. (1984a) G-closure of some particular sets of admissible material characteristics for the problem of bending of thin plates. J. Opt. Th. Appl. 42, 305-316.
    • (1984) J. Opt. Th. Appl. , vol.42 , pp. 305-316
    • Lurie, K.A.1    Cherkaev, A.V.2
  • 21
    • 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. (1984b) Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion. Proc. Roy. Soc. Edinburgh A 99, 71-87.
    • (1984) Proc. Roy. Soc. Edinburgh A , vol.99 , pp. 71-87
    • Lurie, K.A.1    Cherkaev, A.V.2
  • 22
    • 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. Roy. Soc. Edinburgh A 104, 21-38.
    • (1986) Proc. Roy. Soc. Edinburgh A , vol.104 , pp. 21-38
    • Lurie, K.A.1    Cherkaev, A.V.2
  • 23
    • 0002338788 scopus 로고
    • The effective characteristics of composite materials and optimal design of constructions
    • translation to appear in Topics in the Mathematical Modelling of Composite Materials (ed. R. V. Kohn), Birkhauser, NY
    • 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, translation to appear in Topics in the Mathematical Modelling of Composite Materials (ed. R. V. Kohn), Birkhauser, NY.
    • (1986) Advances' in Mechanics (Poland) , vol.9 , pp. 3-81
    • Lurie, K.A.1    Cherkaev, A.V.2
  • 24
    • 0020169555 scopus 로고
    • Regularization of optimal design problems for bars and plates I and II
    • Lurie, K. A, Cherkaev, A. V. and Fedorov, A. V. (1982) Regularization of optimal design problems for bars and plates I and II. J. Opt. Th. Appl. 37, 499-543.
    • (1982) J. Opt. Th. Appl. , vol.37 , pp. 499-543
    • Lurie, K.A.1    Cherkaev, A.V.2    Fedorov, A.V.3
  • 25
    • 0040771898 scopus 로고
    • Linear response of polycrystals to coupled fields : Exact relations among the coefficients
    • Milgrom, M. and Shtrikman, S. (1989) Linear response of polycrystals to coupled fields : exact relations among the coefficients. Phys. Rev. B 40, 5991-5994.
    • (1989) Phys. Rev. B , vol.40 , pp. 5991-5994
    • Milgrom, M.1    Shtrikman, S.2
  • 26
    • 0001507478 scopus 로고
    • Modeling the properties of composites by laminates
    • ed. J. L. Ericksen, D. Kinderlehrer, R. Kohn and J.-L. Lions, Springer-Verlag, New York
    • Milton, G. W. (1986) Modeling the properties of composites by laminates. Homogenization and Effective Moduli of Materials and Media (ed. J. L. Ericksen, D. Kinderlehrer, R. Kohn and J.-L. Lions), pp. 150-174. Springer-Verlag, New York.
    • (1986) Homogenization and Effective Moduli of Materials and Media , pp. 150-174
    • Milton, G.W.1
  • 27
    • 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. of Pure and Appl. Math. XLIII, 63-125.
    • (1990) Comm. of Pure and Appl. Math. , vol.43 , pp. 63-125
    • Milton, G.W.1
  • 28
    • 0041621235 scopus 로고
    • A brief review of the translation method for bounding effective elastic tensors of composites
    • ed. G. A. Maugin
    • Milton, G. W. (1990b) A brief review of the translation method for bounding effective elastic tensors of composites. Continuum Models and Discrete Systems (ed. G. A. Maugin), Vol. 1, pp. 60-74.
    • (1990) Continuum Models and Discrete Systems , vol.1 , pp. 60-74
    • Milton, G.W.1
  • 29
    • 84990648239 scopus 로고
    • A link between sets of tensors stable under lamination and quasiconvexity
    • Milton, G. W. (1994) A link between sets of tensors stable under lamination and quasiconvexity. Comm. Pure Appl. Math. XLVII, 959-1003.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 959-1003
    • Milton, G.W.1
  • 30
    • 0001496391 scopus 로고
    • Calcul des variations et homogeneisation. Les methodes de l'homogeneisation: Theorie et applictions en physique
    • Eyrolles, Paris
    • Murat, F. and Tartar, L. (1985) Calcul des variations et homogeneisation. Les Methodes de l'Homogeneisation: Theorie et Applictions en Physique, Coll. de la Dir. des Etudes et Recherches de Electr. de France, Eyrolles, Paris, 319-370.
    • (1985) Coll. de la Dir. des Etudes et Recherches de Electr. de France , pp. 319-370
    • Murat, F.1    Tartar, L.2
  • 31
    • 0022035002 scopus 로고
    • A differential scheme for the effective moduli of composites
    • Norris, A. N. (1985) A differential scheme for the effective moduli of composites. Mech. Mater. 4, 1-16.
    • (1985) Mech. Mater. , vol.4 , pp. 1-16
    • Norris, A.N.1
  • 32
    • 30244457884 scopus 로고
    • Master's Thesis, St. Petersburg Technical University, St. Petersburg, Russia
    • Rudelson, M. (1989) Phase transitions in solids. Master's Thesis, St. Petersburg Technical University, St. Petersburg, Russia.
    • (1989) Phase Transitions in Solids
    • Rudelson, M.1
  • 33
    • 0002197945 scopus 로고
    • Nonhomogeneous media and vibration theory
    • Springer-Verlag
    • Sanchez-Palencia, E. (1980) Nonhomogeneous media and vibration theory. Lecture Notes in Physics 127, Springer-Verlag.
    • (1980) Lecture Notes in Physics , vol.127
    • Sanchez-Palencia, E.1
  • 34
    • 0000842603 scopus 로고
    • Bounds on the conductivity of statistically isotropic polycrystals
    • Schulgasser, K. (1977) Bounds on the conductivity of statistically isotropic polycrystals. J. Phys. C 10, 407-417.
    • (1977) J. Phys. C , vol.10 , pp. 407-417
    • Schulgasser, K.1
  • 35
    • 0041621231 scopus 로고
    • Thermal expansion of polycrystals
    • Schulgasser, K. (1989) Thermal expansion of polycrystals. J. Mater. Sci. Lett. 8, 228-229.
    • (1989) J. Mater. Sci. Lett. , vol.8 , pp. 228-229
    • Schulgasser, K.1
  • 36
    • 0001156303 scopus 로고
    • Estimation de coefficients homogeneises
    • Computing Methods in Applied Sciences and Engineering Springer-Verlag
    • Tartar, L. (1978) Estimation de coefficients homogeneises. Computing Methods in Applied Sciences and Engineering, pp. 364-373. Lecture Notes in Mathematics 704. Springer-Verlag.
    • (1978) Lecture Notes in Mathematics , vol.704 , pp. 364-373
    • Tartar, L.1
  • 37
    • 0001357333 scopus 로고
    • Estimations fines des coefficients homogeneises
    • Ennio de Giorgi Colloquium (ed. P. Kree)
    • Tartar, L. (1985) Estimations fines des coefficients homogeneises. Ennio de Giorgi Colloquium (ed. P. Kree). Pitman Research Notes in Math. 125, 168-187.
    • (1985) Pitman Research Notes in Math. , vol.125 , pp. 168-187
    • Tartar, L.1
  • 38
    • 49949149864 scopus 로고
    • On bounds for the overall elastic moduli of inhomogeneous systems I and H
    • Walpole, L. (1966) On bounds for the overall elastic moduli of inhomogeneous systems I and H. J. Mech. Phys. Solids 14, 151-162 and 289-301.
    • (1966) J. Mech. Phys. Solids , vol.14 , pp. 151-162
    • Walpole, L.1
  • 40
    • 0002767124 scopus 로고
    • Elasticity theory of composites
    • ed. H. G. Hopkins and M. J. Sewell, Pergamon Press, Oxford
    • Willis, J. R. (1982) Elasticity theory of composites. Mechanics of Solids (ed. H. G. Hopkins and M. J. Sewell), pp. 653-685. Pergamon Press, Oxford.
    • (1982) Mechanics of Solids , pp. 653-685
    • Willis, J.R.1


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