메뉴 건너뛰기




Volumn 455, Issue 1986, 1999, Pages 1993-2020

On anisotropic invariants of N symmetric second-order tensors: Crystal classes and quasi-crystal classes as subgroups of the cylindrical group D∞h

Author keywords

Anisotropy; Crystal classes; Invariants; Quasi crystal classes; Symmetric tensors

Indexed keywords


EID: 0038108269     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0390     Document Type: Article
Times cited : (5)

References (48)
  • 1
    • 0000890511 scopus 로고
    • Dynamic properties of resilient materials: Constitutive equations
    • Adkins, J. E. 1958 Dynamic properties of resilient materials: constitutive equations. Phil. Trans. R. Soc. Land. A 259, 519-541.
    • (1958) Phil. Trans. R. Soc. Land. A , vol.259 , pp. 519-541
    • Adkins, J.E.1
  • 2
    • 0000963311 scopus 로고    scopus 로고
    • 19GOa Symmetry relations for orthotropic and transversely isotropic materials
    • Adkins, J. E. 19GOa Symmetry relations for orthotropic and transversely isotropic materials. Arch. Ration. Mech. Analysis 4, 193-213.
    • Arch. Ration. Mech. Analysis , vol.4 , pp. 193-213
    • Adkins, J.E.1
  • 3
    • 33746760844 scopus 로고
    • Further symmetry relations for transversely isotropic materials
    • Adkins, J. E. 19606 Further symmetry relations for transversely isotropic materials. Arch. Ration. Mech. Analysis 5, 263-274.
    • (1960) Arch. Ration. Mech. Analysis , vol.5 , pp. 263-274
    • Adkins, J.E.1
  • 4
    • 0007545033 scopus 로고
    • Recent advances in applications of tensor functions in solid mechanics
    • Betten, J. 1991 Recent advances in applications of tensor functions in solid mechanics. Adv. Mech. 14, 79-109.
    • (1991) Adv. Mech. , vol.14 , pp. 79-109
    • Betten, J.1
  • 5
    • 33746409999 scopus 로고
    • Kontinuumsmechanik: Elasto-, plasto- Und kriechmechanik
    • Betten, J. 1993 Kontinuumsmechanik: elasto-, plasto- und kriechmechanik. Berlin: Springer.
    • (1993) Berlin: Springer.
    • Betten, J.1
  • 6
    • 0028517012 scopus 로고
    • A physically motivated set of invariants and tensor generators in the case of transverse isotropy
    • Bischoff-Beiermann, B. & Bruhns, O. T. 1994 A physically motivated set of invariants and tensor generators in the case of transverse isotropy. Int. J. Engng Sci. 32, 1531-1552.
    • (1994) Int. J. Engng Sci. , vol.32 , pp. 1531-1552
    • Bischoff-Beiermann, B.1    Bruhns, O.T.2
  • 7
    • 0017497057 scopus 로고
    • On irreducible representations for isotropic scalar functions
    • Boehler, J. P. 1977 On irreducible representations for isotropic scalar functions. Z. Angew. Math. Mech. 57, 323-327.
    • (1977) Z. Angew. Math. Mech. , vol.57 , pp. 323-327
    • Boehler, J.P.1
  • 8
    • 0018155845 scopus 로고
    • Lois de comportement anisotrope des milieux continus
    • Boehler, J. P. 1978 Lois de comportement anisotrope des milieux continus. J. Mécanique 17, 153-190.
    • (1978) J. Mécanique , vol.17 , pp. 153-190
    • Boehler, J.P.1
  • 9
    • 0018454663 scopus 로고
    • A simple derivation of representations for non-polynomial constitutive equations in some cases of anisotropy
    • Boehler, J. P. 1979 A simple derivation of representations for non-polynomial constitutive equations in some cases of anisotropy. Z. Angew. Math. Mech. 59, 157-167.
    • (1979) Z. Angew. Math. Mech. , vol.59 , pp. 157-167
    • Boehler, J.P.1
  • 10
    • 33746467406 scopus 로고
    • Applications of tensor functions in solid mechanics, CISM Courses and Lectures no. 292
    • Boehler, J. P. (ed.)
    • Boehler, J. P. (ed.) 1987 Applications of tensor functions in solid mechanics, CISM Courses and Lectures no. 292. Wien: Springer.
    • (1987) Wien: Springer.
  • 11
    • 0039430295 scopus 로고
    • Representations irréductbles des functions tensorielles anisotropes non-polynomiales de deux tenseurs symétriques
    • Boehler, J. P. & Raclin, J. 1977 Representations irréductbles des functions tensorielles anisotropes non-polynomiales de deux tenseurs symétriques. Arch. Mech. 29, 263-274.
    • (1977) Arch. Mech. , vol.29 , pp. 263-274
    • Boehler, J.P.1    Raclin, J.2
  • 14
    • 0004022578 scopus 로고
    • Foundations of the theory of algebraic invariants
    • Gurevich, G. B. 1964 Foundations of the theory of algebraic invariants. Groningen: Noordhoff.
    • (1964) Groningen: Noordhoff.
    • Gurevich, G.B.1
  • 15
    • 33746434853 scopus 로고
    • Constitutive equations of electromagnetic-elastic crystals
    • Kiral, E. & Bringen, A. C. 1990 Constitutive equations of electromagnetic-elastic crystals. Berlin: Springer.
    • (1990) Berlin: Springer.
    • Kiral, E.1    Bringen, A.C.2
  • 16
    • 0020243053 scopus 로고
    • On representations of anisotropic invariants
    • Liu, I. S. 1982 On representations of anisotropic invariants. Int. J. Engng Sci. 19, 1099-1109.
    • (1982) Int. J. Engng Sci. , vol.19 , pp. 1099-1109
    • Liu, I.S.1
  • 18
    • 0040022578 scopus 로고
    • Material symmetry restrictions on non-polynomial constitutive equations
    • Pipkin, A. C. & Wineman, A. S. 1963 Material symmetry restrictions on non-polynomial constitutive equations. Arch. Ration. Mech. Analysis 12, 420-426.
    • (1963) Arch. Ration. Mech. Analysis , vol.12 , pp. 420-426
    • Pipkin, A.C.1    Wineman, A.S.2
  • 19
    • 0001526377 scopus 로고
    • Further remarks on the stress-deformation relations for isotropic materials
    • Rivlin, R. S. 1955 Further remarks on the stress-deformation relations for isotropic materials. J. Ration. Math. Analysis 4, 681-705.
    • (1955) J. Ration. Math. Analysis , vol.4 , pp. 681-705
    • Rivlin, R.S.1
  • 20
    • 31144463274 scopus 로고
    • Nonlinear viscoelastic solids
    • Rivlin, R. S. 1965o Nonlinear viscoelastic solids. SIAM Rev. 7, 323-340.
    • (1965) SIAM Rev. , vol.7 , pp. 323-340
    • Rivlin, R.S.1
  • 21
    • 84989065162 scopus 로고
    • Viscoelastic fluids
    • ed. G. Temple & R. Seeger, pp. 144-170. New York: Wiley Intersciencc.
    • Rivlin, R. S. 19656 Viscoelastic fluids. In Frontiers of research in fluid dynamics (ed. G. Temple & R. Seeger), pp. 144-170. New York: Wiley Intersciencc.
    • (1965) In Frontiers of Research in Fluid Dynamics
    • Rivlin, R.S.1
  • 22
    • 0001526376 scopus 로고
    • Stress-deformation relations for isotropic materials
    • Rivlin, R. S. & Ericksen, J. L. 1955 Stress-deformation relations for isotropic materials. J. Ration. Mech. Analysis 4, 323-425.
    • (1955) J. Ration. Mech. Analysis , vol.4 , pp. 323-425
    • Rivlin, R.S.1    Ericksen, J.L.2
  • 25
    • 0012767703 scopus 로고
    • On representations of tensor functions: A review
    • Rychlewski, J. & Zhang, J. M. 1991 On representations of tensor functions: a review. Adv. Mech. 14, 75-94.
    • (1991) Adv. Mech. , vol.14 , pp. 75-94
    • Zhang, J.M.1
  • 26
    • 33746668489 scopus 로고
    • On the yield condition for anisotropic materials
    • Smith, G. F. 1962 On the yield condition for anisotropic materials. Q. Appl. Math. 10, 108-118.
    • (1962) Q. Appl. Math. , vol.10 , pp. 108-118
    • Smith, G.F.1
  • 27
    • 0001438758 scopus 로고
    • On isotropic functions of symmetric tensors, skewsymmetric tensors and vectors
    • Smith, G. F. 1971 On isotropic functions of symmetric tensors, skewsymmetric tensors and vectors. Int. J. Engng Sci. 9, 899-916.
    • (1971) Int. J. Engng Sci. , vol.9 , pp. 899-916
    • Smith, G.F.1
  • 28
    • 33746672050 scopus 로고
    • Constitutive equations of anisotropic and isotropic materials
    • Smith, G. F. 1994 Constitutive equations of anisotropic and isotropic materials. New York: Elsevier.
    • (1994) New York: Elsevier.
    • Smith, G.F.1
  • 29
    • 0342397740 scopus 로고
    • Integrity bases for N symmetric second-order tensors: The crystal classes
    • Smith, G. F. & Kiral, E. 1969 Integrity bases for N symmetric second-order tensors: the crystal classes. Rend. Circ. Mat. Palermo II 18, 5-22.
    • (1969) Rend. Circ. Mat. Palermo II , vol.18 , pp. 5-22
    • Smith, G.F.1    Kiral, E.2
  • 30
    • 84968475548 scopus 로고
    • The strain-energy function for anisotropic elastic materials
    • Smith, G. F. & Rivlin, R. S. 1958 The strain-energy function for anisotropic elastic materials. Trans. Am. Math. Soc. 88, 175-193.
    • (1958) Trans. Am. Math. Soc. , vol.88 , pp. 175-193
    • Smith, G.F.1    Rivlin, R.S.2
  • 31
    • 33746440503 scopus 로고
    • The invariants of six symmetric 3x3 matrices
    • Spencer, A. J. M. 1961 The invariants of six symmetric 3x3 matrices. Arch. Ration. Mech. Analysis 17, 64-77.
    • (1961) Arch. Ration. Mech. Analysis , vol.17 , pp. 64-77
    • Spencer, A.J.M.1
  • 33
    • 34250959542 scopus 로고
    • The theory of matrix polynomials and its applications to the mechanics of isotropic continua
    • Spencer, A. J. M. & Rivlin, R. S. 1959a The theory of matrix polynomials and its applications to the mechanics of isotropic continua. Arch. Ration. Mech. Analysis 2, 309-336.
    • (1959) Arch. Ration. Mech. Analysis , vol.2 , pp. 309-336
    • Spencer, A.J.M.1    Rivlin, R.S.2
  • 34
    • 0001553278 scopus 로고
    • Finite integrity:bases for five or fewer symmetric 3x3 matrices
    • Spencer, A. J. M. & Rivlin, R. S. 19596 Finite integrity:bases for five or fewer symmetric 3x3 matrices. Arch. Ration. Mech. Analysis 2, 435-446.
    • (1959) Arch. Ration. Mech. Analysis , vol.2 , pp. 435-446
    • Spencer, A.J.M.1    Rivlin, R.S.2
  • 35
    • 34250959133 scopus 로고
    • Further results in the theory of matrix polynomials
    • Spencer, A. J. M. & Rivlin, R. S. 1960 Further results in the theory of matrix polynomials. Arch. Ration. Mech. Analysis 4, 214-230.
    • (1960) Arch. Ration. Mech. Analysis , vol.4 , pp. 214-230
    • Spencer, A.J.M.1    Rivlin, R.S.2
  • 38
    • 34250494619 scopus 로고
    • A new representation theorem for isotropic functions
    • Corrigendum. Arch. Ration. Mech. Analysis 43, 392-395.
    • Wang, C. C. 1970 A new representation theorem for isotropic functions. I. Scalar-valued isotropic functions. Arch. Ration. Mech. Analysis 36, 166-197. (Corrigendum. Arch. Ration. Mech. Analysis 43, 392-395.)
    • (1970) I. Scalar-valued Isotropic Functions. Arch. Ration. Mech. Analysis , vol.36 , pp. 166-197
    • Wang, C.C.1
  • 40
    • 0009287225 scopus 로고
    • Material symmetry restriction on constitutive equations
    • Wineman, A. S. & Pipkin, A. C. 1964 Material symmetry restriction on constitutive equations. Arch. Ration. Mech. Analysis 17, 184-214.
    • (1964) Arch. Ration. Mech. Analysis , vol.17 , pp. 184-214
    • Wineman, A.S.1    Pipkin, A.C.2
  • 41
    • 0040022577 scopus 로고    scopus 로고
    • On anisotropic scalar functions of a single symmetric tensor
    • Xiao, H. 1996a On anisotropic scalar functions of a single symmetric tensor. Proc. R. Soc. Land. A 452, 1545-1561.
    • (1996) Proc. R. Soc. Land. A , vol.452 , pp. 1545-1561
    • Xiao, H.1
  • 42
    • 33747796882 scopus 로고    scopus 로고
    • 1996& Two general representation theorems for arbitrary-order tensor-valued isotropic and anisotropic tensor functions of vectors and second-order tensors
    • Xiao, H. 1996& Two general representation theorems for arbitrary-order tensor-valued isotropic and anisotropic tensor functions of vectors and second-order tensors. Z. Angew. Math. Mech. 76, 151-161.
    • Z. Angew. Math. Mech. , vol.76 , pp. 151-161
    • Xiao, H.1
  • 43
    • 21344441069 scopus 로고    scopus 로고
    • On isotropic extension of anisotropic tensor functions
    • Xiao, H. 1996c On isotropic extension of anisotropic tensor functions. Z. Angew. Math. Mech. 76, 205-215.
    • (1996) Z. Angew. Math. Mech. , vol.76 , pp. 205-215
    • Xiao, H.1
  • 44
    • 0038447567 scopus 로고    scopus 로고
    • On anisotropic invariants of a single symmetric tensor: Crystal classes, quasi-crystal classes and others
    • Xiao, H. 1997a On anisotropic invariants of a single symmetric tensor: crystal classes, quasi-crystal classes and others. Proc. R. Soc. Lond. A 454, 1217-1240.
    • (1997) Proc. R. Soc. Lond. A , vol.454 , pp. 1217-1240
    • Xiao, H.1
  • 45
    • 0038447568 scopus 로고    scopus 로고
    • A unified theory of representations for scalar-, vector- And second-order tensorvalued anisotropic tensor functions of vectors and second-order tensors
    • Xiao, H. 19976 A unified theory of representations for scalar-, vector- and second-order tensorvalued anisotropic tensor functions of vectors and second-order tensors. Arch. Mech. 49, 995-1039.
    • (1997) Arch. Mech. , vol.49 , pp. 995-1039
    • Xiao, H.1
  • 46
    • 0027675525 scopus 로고
    • On transversely isotropic, orthotropic and relatively isotropic functions of symmetric tensors, skewsymmetric tensors and vectors
    • Zheng, Q. S. 1993 On transversely isotropic, orthotropic and relatively isotropic functions of symmetric tensors, skewsymmetric tensors and vectors. I-V. Int. J. Engng Sci. 32, 1399-1453.
    • (1993) I-V. Int. J. Engng Sci. , vol.32 , pp. 1399-1453
    • Zheng, Q.S.1
  • 47
    • 85025220892 scopus 로고
    • Theory of tensor function representations: A unified invariant approach to constitutive equations
    • Zheng, Q. S. 1994 Theory of tensor function representations: a unified invariant approach to constitutive equations. Appl. Mech. Rev. 47, 545-587.
    • (1994) Appl. Mech. Rev. , vol.47 , pp. 545-587
    • Zheng, Q.S.1
  • 48
    • 51249164024 scopus 로고
    • Tensor function representations as applied to constitutive laws for clinotropic materials
    • Zheng, Q. S. & Boehler, J. P. 1994 Tensor function representations as applied to constitutive laws for clinotropic materials. Acta Mech. Sinica 10, 336-348.
    • (1994) Acta Mech. Sinica , vol.10 , pp. 336-348
    • Zheng, Q.S.1    Boehler, J.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.