Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

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 | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [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 $ H\left( A \right) = \alpha I + \beta A \\ + \gamma {A^2}$ 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 $ H\left( A \right) = \alpha I + \beta A + \gamma {A^2}$ for isotropic tensor functions of class $ {C^r}$, J. Elasticity (to appear)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73B05, 15A72, 15A90, 73C50

Retrieve articles in all journals with MSC: 73B05, 15A72, 15A90, 73C50


Additional Information

DOI: https://doi.org/10.1090/qam/1373842
Article copyright: © Copyright 1996 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website