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Volumn 48, Issue 3, 1997, Pages 241-283

On Constitutive Equations of Cauchy Elastic Solids: All Kinds of Crystals and Quasicrystals

Author keywords

Cauchy elasticity; Constitutive equation; Crystals; Nonpolynomial representation; Quasicrystals; Symmetry restriction

Indexed keywords

CRYSTALS; POLYNOMIALS; QUASICRYSTALS; TENSORS;

EID: 0031333089     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007426414686     Document Type: Article
Times cited : (12)

References (47)
  • 1
    • 0001314297 scopus 로고
    • A mathematical theory of dilatancy
    • M. Reiner, A mathematical theory of dilatancy. Am. J. Math. 67 (1945) 350-362.
    • (1945) Am. J. Math. , vol.67 , pp. 350-362
    • Reiner, M.1
  • 2
    • 0001503470 scopus 로고
    • Elasticity beyond the elastic limit
    • M. Reiner, Elasticity beyond the elastic limit. Am. J. Math. 70 (1948) 433-446.
    • (1948) Am. J. Math. , vol.70 , pp. 433-446
    • Reiner, M.1
  • 3
    • 84979325887 scopus 로고
    • Das isotrope Elastizitatsgesetz
    • H. Richter, Das isotrope Elastizitatsgesetz. Zeits. Angew. Math. Mech. 28 (1948) 205-209.
    • (1948) Zeits. Angew. Math. Mech. , vol.28 , pp. 205-209
    • Richter, H.1
  • 4
    • 0001526376 scopus 로고
    • Stress-deformation relations for isotropic materials
    • R.S. Rivlin and J.L. Ericksen, Stress-deformation relations for isotropic materials. J. Rat. Mech. Anal. 4 (1955) 323-425.
    • (1955) J. Rat. Mech. Anal. , vol.4 , pp. 323-425
    • Rivlin, R.S.1    Ericksen, J.L.2
  • 5
    • 2342631763 scopus 로고
    • Stress-deformation relations for anisotropic solids
    • G.F. Smith and R.S. Rivlin, Stress-deformation relations for anisotropic solids. Arch. Rat. Mech. Anal. 1 (1957) 107-112.
    • (1957) Arch. Rat. Mech. Anal. , vol.1 , pp. 107-112
    • Smith, G.F.1    Rivlin, R.S.2
  • 6
    • 84968475548 scopus 로고
    • The strain-energy function for anisotropic elastic materials
    • G.F. Smith and R.S. Rivlin, The strain-energy function for anisotropic elastic materials. Trans. Amer. Math. Soc. 88 (1958) 175-193.
    • (1958) Trans. Amer. Math. Soc. , vol.88 , pp. 175-193
    • Smith, G.F.1    Rivlin, R.S.2
  • 7
    • 0000227803 scopus 로고
    • The formulation of constitutive equations in continuum physics
    • A.C. Pipkin and R.S. Rivlin, The formulation of constitutive equations in continuum physics. Arch. Rat. Mech. Anal. 4 (1959) 129-144.
    • (1959) Arch. Rat. Mech. Anal. , vol.4 , pp. 129-144
    • Pipkin, A.C.1    Rivlin, R.S.2
  • 8
    • 0000198210 scopus 로고
    • The derivation of stress-deformation relations for a Stokesian fluid
    • J. Serrin, The derivation of stress-deformation relations for a Stokesian fluid. J. Math. Mech. 8 (1959) 459-468.
    • (1959) J. Math. Mech. , vol.8 , pp. 459-468
    • Serrin, J.1
  • 9
    • 0000963311 scopus 로고
    • Symmetry relations for orthotropic and transversely isotropic materials
    • J.E. Adkins, Symmetry relations for orthotropic and transversely isotropic materials. Arch. Rat. Mech. Anal. 4 (1960) 193-213.
    • (1960) Arch. Rat. Mech. Anal. , vol.4 , pp. 193-213
    • Adkins, J.E.1
  • 10
    • 33746760844 scopus 로고
    • Further symmetry relations for transversely isotropic materials
    • J.E. Adkins, Further symmetry relations for transversely isotropic materials. Arch. Rat. Mech. Anal. 5 (1960) 263-274.
    • (1960) Arch. Rat. Mech. Anal. , vol.5 , pp. 263-274
    • Adkins, J.E.1
  • 11
    • 10444251895 scopus 로고
    • Transversely isotropic fluids
    • J.L. Ericksen, Transversely isotropic fluids. Kolloid Zeitschrift 173 (1960) 117-122.
    • (1960) Kolloid Zeitschrift , vol.173 , pp. 117-122
    • Ericksen, J.L.1
  • 12
    • 33746668489 scopus 로고
    • Further results on the strain-energy function for anisotropic elastic materials
    • G.F. Smith, Further results on the strain-energy function for anisotropic elastic materials. Arch. Rat. Mech. Anal. 10 (1962) 108-118.
    • (1962) Arch. Rat. Mech. Anal. , vol.10 , pp. 108-118
    • Smith, G.F.1
  • 13
    • 0040022578 scopus 로고
    • Material symmetry restrictions on non-polynomial constitutive equations
    • A.C. Pipkin and A.S. Wineman, Material symmetry restrictions on non-polynomial constitutive equations. Arch. Rat. Mech. Anal. 12 (1963) 420-426.
    • (1963) Arch. Rat. Mech. Anal. , vol.12 , pp. 420-426
    • Pipkin, A.C.1    Wineman, A.S.2
  • 14
    • 0009287225 scopus 로고
    • Material symmetry restrictions on constitutive equations
    • A.S. Wineman and A.C. Pipkin, Material symmetry restrictions on constitutive equations. Arch. Rat. Mech. Anal. 17 (1964) 184-214.
    • (1964) Arch. Rat. Mech. Anal. , vol.17 , pp. 184-214
    • Wineman, A.S.1    Pipkin, A.C.2
  • 15
    • 2342589926 scopus 로고
    • A continuum theory of anisotropic fluids
    • A.E. Green, A continuum theory of anisotropic fluids. Proc. Camb. Phil. Soc. 60 (1964) 123-128.
    • (1964) Proc. Camb. Phil. Soc. , vol.60 , pp. 123-128
    • Green, A.E.1
  • 16
    • 0002565890 scopus 로고
    • The Nonlinear Field Theories of Mechanics
    • S. Flügge (ed.), Berlin; Springer-Verlag
    • C. Truesdell and W. Noll, The Nonlinear Field Theories of Mechanics. In: S. Flügge (ed.), Handbuch der Physik, Bd. III/3, Berlin; Springer-Verlag (1965).
    • (1965) Handbuch der Physik , vol.3 , Issue.3
    • Truesdell, C.1    Noll, W.2
  • 17
    • 0001416793 scopus 로고
    • Theory of Invariants
    • A.C. Eringen (ed.), New York: Academic Press
    • A.J.M. Spencer, Theory of Invariants. In: A.C. Eringen (ed.), Continuum Physics, Vol. I. New York: Academic Press (1971).
    • (1971) Continuum Physics , vol.1
    • Spencer, A.J.M.1
  • 20
    • 0004327536 scopus 로고
    • CBMS 35, SIAM, second printing, Berlin, New Jersey: Hamilton Press
    • M.E. Gurtin, Topics in Finite Elasticity. CBMS 35, SIAM, second printing, Berlin, New Jersey: Hamilton Press (1993).
    • (1993) Topics in Finite Elasticity
    • Gurtin, M.E.1
  • 21
    • 0018454663 scopus 로고
    • A simple derivation of representations for non-polynomial constitutive equations in some cases of anisotropy
    • J.P. Boehler, A simple derivation of representations for non-polynomial constitutive equations in some cases of anisotropy. Zeits. Angew. Math. Mech. 59 (1979) 157-167.
    • (1979) Zeits. Angew. Math. Mech. , vol.59 , pp. 157-167
    • Boehler, J.P.1
  • 22
    • 0020243053 scopus 로고
    • On representations of anisotropic invariants
    • I-Shih Liu, On representations of anisotropic invariants. Int. J. Engng Sci. 20 (1982) 1099-1109.
    • (1982) Int. J. Engng Sci. , vol.20 , pp. 1099-1109
    • Liu, I.-S.1
  • 23
    • 84972553380 scopus 로고
    • Differentiability properties of symmetric and isotropic functions
    • J.M. Ball, Differentiability properties of symmetric and isotropic functions. Duke Math. J. 51 (1984) 699-728.
    • (1984) Duke Math. J. , vol.51 , pp. 699-728
    • Ball, J.M.1
  • 24
    • 0022187159 scopus 로고
    • Tensor function representations as applied to deriving constitutive relations for skewed anisotropy
    • M. Basista, Tensor function representations as applied to deriving constitutive relations for skewed anisotropy. Zeits. Angew. Math. Mech. 65 (1985) 151-158.
    • (1985) Zeits. Angew. Math. Mech. , vol.65 , pp. 151-158
    • Basista, M.1
  • 26
    • 0028517012 scopus 로고
    • A physically motivated set of invariants and tensor generators in the case of transverse isotropy
    • B. Bischoff-Beiermann and O.T. Bruhns, A physically motivated set of invariants and tensor generators in the case of transverse isotropy. Int. J. Engng Sci. 32 (1994) 1531-1552.
    • (1994) Int. J. Engng Sci. , vol.32 , pp. 1531-1552
    • Bischoff-Beiermann, B.1    Bruhns, O.T.2
  • 27
    • 0028383606 scopus 로고
    • 2 for isotropic tensor functions
    • 2 for isotropic tensor functions. J. Elasticity 34 (1994) 229-238.
    • (1994) J. Elasticity , vol.34 , pp. 229-238
    • Man, C.-S.1
  • 29
    • 0027675525 scopus 로고
    • On transversely isotropic, orthotropic and relatively isotropic functions of symmetric tensors, skewsymmetric tensors and vectors. Part I-V
    • Q.S. Zheng, On transversely isotropic, orthotropic and relatively isotropic functions of symmetric tensors, skewsymmetric tensors and vectors. Part I-V. Int. J. Engng Sci. 31 (1993) 1399-1453.
    • (1993) Int. J. Engng Sci. , vol.31 , pp. 1399-1453
    • Zheng, Q.S.1
  • 30
    • 0012767703 scopus 로고
    • On representations of tensor functions: A review
    • Jan Rychlewski and J.M. Zhang, On representations of tensor functions: A review. Advances in Mechanics 14(4) (1991) 75-94.
    • (1991) Advances in Mechanics , vol.14 , Issue.4 , pp. 75-94
    • Rychlewski, J.1    Zhang, J.M.2
  • 31
    • 85025220892 scopus 로고
    • Theory of tensor function representations: A unified invariant approach to constitutive equations
    • Q.S. Zheng, Theory of tensor function representations: A unified invariant approach to constitutive equations. Appl. Mech. Rev. 47 (1994) 545-587.
    • (1994) Appl. Mech. Rev. , vol.47 , pp. 545-587
    • Zheng, Q.S.1
  • 34
    • 0038757423 scopus 로고
    • Finding the finite groups of symmetries of the sphere
    • M. Senechal, Finding the finite groups of symmetries of the sphere. Amer. Math. Monthly 97 (1990) 329-335.
    • (1990) Amer. Math. Monthly , vol.97 , pp. 329-335
    • Senechal, M.1
  • 37
    • 34250491112 scopus 로고
    • A new representation theorem for isotropic functions. Part II
    • C.C. Wang, A new representation theorem for isotropic functions. Part II. Arch. Rat. Mech. Anal. 36 (1970) 198-223.
    • (1970) Arch. Rat. Mech. Anal. , vol.36 , pp. 198-223
    • Wang, C.C.1
  • 38
    • 2342518653 scopus 로고
    • A general representation theorem for anisotropic invariants
    • W. Z. Chien et al (eds), Beijing: Peking University Press
    • H. Xiao and Z.H. Guo, A general representation theorem for anisotropic invariants. In: W. Z. Chien et al (eds), Proceedings of the 2nd International Conference on Nonlinear Mechanics, pp. 206-210. Beijing: Peking University Press (1993).
    • (1993) Proceedings of the 2nd International Conference on Nonlinear Mechanics , pp. 206-210
    • Xiao, H.1    Guo, Z.H.2
  • 39
    • 2342581972 scopus 로고
    • A unified theory of representations for anisotropic tensor function of vectors and second order tensors
    • Beijing
    • H. Xiao, A unified theory of representations for anisotropic tensor function of vectors and second order tensors. Peking University Dept. of Math. and Inst. of Math. Research Report No. 8, Beijing (1995); Arch. Mech. (in press).
    • (1995) Peking University Dept. of Math. and Inst. of Math. Research Report , vol.8
    • Xiao, H.1
  • 40
    • 2342459538 scopus 로고    scopus 로고
    • in press
    • H. Xiao, A unified theory of representations for anisotropic tensor function of vectors and second order tensors. Peking University Dept. of Math. and Inst. of Math. Research Report No. 8, Beijing (1995); Arch. Mech. (in press).
    • Arch. Mech.
  • 41
    • 0029288876 scopus 로고
    • General irreducible representations for constitutive equations of elastic crystals and transversely isotropic elastic solids
    • H. Xiao, General irreducible representations for constitutive equations of elastic crystals and transversely isotropic elastic solids. J. Elasticity 39 (1995) 47-73.
    • (1995) J. Elasticity , vol.39 , pp. 47-73
    • Xiao, H.1
  • 42
    • 33747796882 scopus 로고    scopus 로고
    • Two general representation theorems for arbitrary-order-tensor-valued isotropic and anisotropic tensor functions of vectors and second order tensors
    • H. Xiao, Two general representation theorems for arbitrary-order-tensor-valued isotropic and anisotropic tensor functions of vectors and second order tensors. Zeits. Angew. Math. Mech. 76 (1996) 151-162.
    • (1996) Zeits. Angew. Math. Mech. , vol.76 , pp. 151-162
    • Xiao, H.1
  • 43
    • 21344441069 scopus 로고    scopus 로고
    • On isotropic extension of anisotropic tensor functions
    • H. Xiao, On isotropic extension of anisotropic tensor functions. Zeits. Angew. Math. Mech. 76 (1996) 205-214.
    • (1996) Zeits. Angew. Math. Mech. , vol.76 , pp. 205-214
    • Xiao, H.1
  • 44
    • 0040022577 scopus 로고    scopus 로고
    • On representations of anisotropic scalar functions of a single symmetric tensor
    • H. Xiao, On representations of anisotropic scalar functions of a single symmetric tensor. Proc. Roy. Soc. London A 452 (1996) 1545-1561.
    • (1996) Proc. Roy. Soc. London A , vol.452 , pp. 1545-1561
    • Xiao, H.1
  • 45
    • 0030261294 scopus 로고    scopus 로고
    • On minimal representations for constitutive equations of anisotropic elastic materials
    • H. Xiao, On minimal representations for constitutive equations of anisotropic elastic materials. J. Elasticity 45 (1996) 13-32.
    • (1996) J. Elasticity , vol.45 , pp. 13-32
    • Xiao, H.1
  • 46
    • 2342643286 scopus 로고    scopus 로고
    • On anisotropic invariants of a single symmetric tensor: Crystal classes, quasicrystal classes and others
    • in press
    • H. Xiao, On anisotropic invariants of a single symmetric tensor: crystal classes, quasicrystal classes and others. Proc. Roy. Soc. London A. (in press).
    • Proc. Roy. Soc. London A
    • Xiao, H.1
  • 47
    • 3242853421 scopus 로고    scopus 로고
    • Further results on general representation theorems for arbitrary-order-tensor-valued isotropic and anisotropic tensor functions of vectors and second order tensors
    • to appear
    • H. Xiao, Further results on general representation theorems for arbitrary-order-tensor-valued isotropic and anisotropic tensor functions of vectors and second order tensors. Zeits. Angew. Math. Mech. (to appear).
    • Zeits. Angew. Math. Mech.
    • Xiao, H.1


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