Differentiability of the scalar coefficients in two representation formulae for isotropic tensor functions in two dimensions

Authors:
Chi-Sing Man and Jeffrey B. Schanding

Journal:
Quart. Appl. Math. **54** (1996), 121-132

MSC:
Primary 73B05; Secondary 15A72, 15A90, 73C50

DOI:
https://doi.org/10.1090/qam/1373842

MathSciNet review:
MR1373842

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References | Similar Articles | Additional Information

**[1]**C.-C. Wang,*A new representation theorem for isotropic functions. Part 1*, Arch. Rational Mech. Anal.**36**, 166-197 (1970)**[2]**C.-C. Wang,*A new representation theorem for isotropic functions. Part 2*, Arch. Rational Mech. Anal.**36**, 198-223 (1970)**[3]**G. F. Smith,*On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors*, Internat. J. Engrg. Sci.**9**, 899-916 (1971)**[4]**J. Serrin,*The derivation of stress-deformation relations for a Stokesian fluid*, J. Math. Mech.**8**, 459-468 (1959)**[5]**C.-S. Man,*Remarks on the continuity of the scalar coefficients in the representation for isotropic tensor functions*, J. Elasticity**34**, 229-238 (1994)**[6]**J. M. Ball,*Differentiability properties of symmetric and isotropic functions*, Duke Math. J.**51**, 699-728 (1984)**[7]**R. S. Rivlin and J. L. Ericksen,*Stress-deformation relations for isotropic materials*, J. Rational Mech. Anal.**4**, 323-424 (1955)**[8]**W. Noll,*On the continuity of the solid and fluid states*, J. Rational Mech. Anal.**4**, 3-81 (1955)**[9]**C.-S. Man,*On the acoustoelastic earing coefficient of plastically prestrained sheets*, Proceedings of the 2nd International Conference on Nonlinear Mechanics, Wei-zang Chien et al. (eds.), Peking University Press, Beijing, China, 1993, pp. 66-71**[10]**H. Whitney,*Differentiability of the remainder term in Taylor's formula*, Duke Math. J.**10**, 153-158 (1943)**[11]**C. Truesdell and W. Noll,*The non-linear field theories of mechanics*, vol. III/3 of S. Flügge's Encyclopedia of Physics, Springer-Verlag, Berlin, 1965**[12]**C.-S. Man,*Smoothness of the scalar coefficients in the representation for isotropic tensor functions of class*, J. Elasticity (to appear)

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DOI:
https://doi.org/10.1090/qam/1373842

Article copyright:
© Copyright 1996
American Mathematical Society