journal article·1996-10

On minimal representations for constitutive equations of anisotropic elastic materials

Heng Xiao

Journal of Elasticity· Volume 45· Issue 1
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OpenAlex topics: Elasticity and Material Modeling · Elasticity and Wave Propagation · Composite Material Mechanics

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References (35)

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1. M. Reiner, A mathematical theory of dilatency. Am. J. Math. 67 (1945) 350–362.10.2307/2371950 ↗
2. M. Reiner, Elasticity beyond the elastic limit. Am. J. Math. 70 (1948) 433–446.10.2307/2372342 ↗
3. H. Richter, Das isotrope Elastizitatsgesetz. Zeits. angew. Math. Mech. 28 (1948) 205–209.10.1002/zamm.19480280703 ↗
4. R.S. Rivlin and J.L. Ericksen, Stress-deformation relations for isotropic materials. J. Rat. Mech. Anal. 4 (1955) 323–425.
5. G.F. Smith and R.S. Rivlin, Stress-deformation relations for anisotropic solids. Arch. Rat. Mech. Anal. 1 (1957) 107–112.10.1007/BF00297999 ↗
6. G.F. Smith and R.S. Rivlin, The strain-energy function for anisotropic elastic materials. Trans. Amer. Math. Soc. 88 (1958) 175–193.10.1090/S0002-9947-1958-0095618-2 ↗
7. J. Serrin, The derivation of the stress-deformation relations for a Stokesian fluid. J. Math. Mech. 8 (1959) 459–468.
8. J.L. Ericksen, Transversely isotropic fluids. Kolloid Zeitschrift 173 (1960) 117–122.10.1007/BF01502416 ↗
9. G.F. Smith, Further results on the strain-energy function for anisotropic elastic materials. Arch. Rat. Mech. Anal. 10 (1962) 108–118.10.1007/BF00281180 ↗
10. A.C. Pipkin and A.S. Wineman, Material symmetry restrictions on non-polynomial constitutive equations. Arch Rat. Mech. Anal. 12 (1963) 420–426.10.1007/BF00281238 ↗
11. A.S. Wineman and A.C. Pipkin, Material symmetry restrictions on constitutive equations. Arch. Rat. Mech. Anal. 17 (1964) 184–214.10.1007/BF00282437 ↗
12. A.E. Green, A continuum theory of anisotropic fluids. Proc. Camb. Phil. Soc. 60 (1964) 123–128.10.1017/S0305004100037531 ↗
13. A.J.M. Spencer, Theory of Invariants. In: A.C. Eringen (ed.), Continuum Physics, Vol. I. Academic Press, New York (1971).
14. C.C. Wang, A new representation theorem for isotropic functions. Part I and II. Arch. Rat. Mech. Anal. 36 (1970) 166–223. Corrigendum. ibid 43 (1971) 292–295.10.1007/BF00272241 ↗
15. G.F. Smith, On isotropic functions of symmetric tensors, skewsymmetric tensors, and vectors. Int. J. Engng Sci. 9 (1971) 899–916.10.1016/0020-7225(71)90023-1 ↗
16. J.P. Boehler, On irreducible representations for isotropic scalar functions. Zeits. angew. Math. Mech. 57 (1977) 323–327.10.1002/zamm.19770570608 ↗
17. J.P. Boehler, A simple derivation of representations for non-polynomial constitutive equations in some cases of anisotropy. Zeits. angew. Math. Mech. 59 (1979) 157–167.10.1002/zamm.19790590403 ↗
18. M.E. Gurtin, Introduction to Mechanics of Continuous Media. Academic Press, New York (1981).
19. I-Shih Liu, On representations of anisotropic invariants. Int. J. Engng Sci. 20 (1982) 1099–1109.10.1016/0020-7225(82)90092-1 ↗
20. J.M. Ball, Differentiability properties of symmetric and isotropic functions. Duke Math. J. 51 (1984) 699–728.10.1215/S0012-7094-84-05134-2 ↗
21. J.P. Boehler (ed.), Applications of Tensor Functions in Solid Mechanics. Springer-Verlag, New York and Wien (1987).
22. S. Pennisi and M. Trovato, On irreducibility of Professor G. F. Smith's representations for isotropic functions. Int. J. Engng Sci. 25 (1987) 1059–1065.10.1016/0020-7225(87)90097-8 ↗
23. 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) 1899–1453.
24. 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) 1531–1552.10.1016/0020-7225(94)90162-7 ↗
25. Q.S. Zheng and J.P. Boehler, Description, classification and physical reality of material and physical symmetries. Acta Mechanica 102 (1994) 73–89.10.1007/BF01178519 ↗
26. Q.S. Zheng and J.P. Boehler, Tensor function representations as applied to constitutive laws for clinotropic materials. Acta Mechanica Sinica 10 (1994) 336–348.10.1007/BF02487658 ↗
27. Q.S. Zheng, Theory of representations for tensor functions: A unified invariant approach to constitutive equations. Appl. Mech. Rev. 47 (1994) 545–587.10.1115/1.3111066 ↗
28. C.-S. Man, Remarks on the continuity of the scalar coefficients in the representation H(A)=αI+βA+γA 2 for isotropic tensor functions. J. Elasticity 34 (1994) 229–238.10.1007/BF00040765 ↗
29. C.-S. Man, Smoothness of the scalar coefficients in the representation H(A)=αI+βA+γA 2 for isotropic tensor functions of class C r . J. Elasticity 40 (1995) 165–182.10.1007/BF00042459 ↗
30. C.-S. Man and J.B. Schanding, Differentiability of the scalar coefficients in two representation formulae for isotropic functions in two dimensions. Quart. Appl. Math. (1996), to appear.10.1090/qam/1373842 ↗
31. H. Xiao and Z.H. Guo, A general representation theorem for anisotropic invariants. In: W.Z. Chien, Z.H. Guo, and Y.Z. Guo (eds.), Proceedings of the 2nd International Conference on Nonlinear Mechanics. Peking University Press, Beining (1993) 206–210.
32. H. Xiao, General irreducible representations for constitutive equations of elastic crystals and transversely isotropic elastic solids. J. Elasticity 39 (1995) 47–73.10.1007/BF00042441 ↗
33. H. Xiao, a unified theory of representations for anisotropic tensor functions of vectors and second order tensors. Peking Univ. Dept. of Math. Research Report No. 8 (1995).
34. H. Xiao, On isotropic extension of anisotropic tensor functions. Zeits. angew. Math. Mech. 76 (1996) 205–214.10.1002/zamm.19960760403 ↗
35. H. Xiao, On representations of anisotropic scalar functions of a single symmetric second order tensor. Proc. Roy. Soc. London A (1996) 1545–1561.10.1098/rspa.1996.0082 ↗