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
Full-text PDF Free Access
References |
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Additional Information
C.-C. Wang, A new representation theorem for isotropic functions. Part 1, Arch. Rational Mech. Anal. 36, 166–197 (1970)
C.-C. Wang, A new representation theorem for isotropic functions. Part 2, Arch. Rational Mech. Anal. 36, 198–223 (1970)
G. F. Smith, On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors, Internat. J. Engrg. Sci. 9, 899–916 (1971)
J. Serrin, The derivation of stress-deformation relations for a Stokesian fluid, J. Math. Mech. 8, 459–468 (1959)
C.-S. Man, Remarks on the continuity of the scalar coefficients in the representation $H\left ( A \right ) = \alpha I + \beta A \\ + \gamma {A^2}$ for isotropic tensor functions, J. Elasticity 34, 229–238 (1994)
J. M. Ball, Differentiability properties of symmetric and isotropic functions, Duke Math. J. 51, 699–728 (1984)
R. S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Rational Mech. Anal. 4, 323–424 (1955)
W. Noll, On the continuity of the solid and fluid states, J. Rational Mech. Anal. 4, 3–81 (1955)
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
H. Whitney, Differentiability of the remainder term in Taylor’s formula, Duke Math. J. 10, 153–158 (1943)
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
C.-S. Man, Smoothness of the scalar coefficients in the representation $H\left ( A \right ) = \alpha I + \beta A + \gamma {A^2}$ for isotropic tensor functions of class ${C^r}$, J. Elasticity (to appear)
C.-C. Wang, A new representation theorem for isotropic functions. Part 1, Arch. Rational Mech. Anal. 36, 166–197 (1970)
C.-C. Wang, A new representation theorem for isotropic functions. Part 2, Arch. Rational Mech. Anal. 36, 198–223 (1970)
G. F. Smith, On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors, Internat. J. Engrg. Sci. 9, 899–916 (1971)
J. Serrin, The derivation of stress-deformation relations for a Stokesian fluid, J. Math. Mech. 8, 459–468 (1959)
C.-S. Man, Remarks on the continuity of the scalar coefficients in the representation $H\left ( A \right ) = \alpha I + \beta A \\ + \gamma {A^2}$ for isotropic tensor functions, J. Elasticity 34, 229–238 (1994)
J. M. Ball, Differentiability properties of symmetric and isotropic functions, Duke Math. J. 51, 699–728 (1984)
R. S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Rational Mech. Anal. 4, 323–424 (1955)
W. Noll, On the continuity of the solid and fluid states, J. Rational Mech. Anal. 4, 3–81 (1955)
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
H. Whitney, Differentiability of the remainder term in Taylor’s formula, Duke Math. J. 10, 153–158 (1943)
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
C.-S. Man, Smoothness of the scalar coefficients in the representation $H\left ( A \right ) = \alpha I + \beta A + \gamma {A^2}$ for isotropic tensor functions of class ${C^r}$, J. Elasticity (to appear)
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Article copyright:
© Copyright 1996
American Mathematical Society
