Abstract
Induced anisotropy is a phenomenon of great interest especially when large continuum elasto-viscoplastic deformations are considered. An initially isotropic continuum can exhibit, as the deformation evolves, stress or deformation induced anisotropies. Accordingly, the kind of anisotropy one is given is defined with respect to the actual configuration and not with respect to the initial one. Hence, it is motivated to discuss the conditions under which the formulation of a free energy function in terms of spatial strain tensors is admissible.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. P. Boehler, Applications of Tensor Functions in Solid Mechanics, Springer-Verlag, Wien 1987.
H. Buller, The Biot stresses in nonlinear elasticity and the associated generalized variational principles, Ing. Arch. 55 (1985) 450–462.
A. C. Eringen, Continuum Physics II, Academic Press, New York 1975.
C. Sansour, On the geometric structure of stress and strain tensors, dual variables and objective rates in continuum mechanics, Arch. Mech. 44 (1992) 527–556.
C. Sansour, On the dual variable of the Cauchy stress tensor and the geometry of deformations, (1994) submitted.
C. Sansour, Induced anisotropy and the formulation of free energy functions in terms of spatial tensors, (1994) submitted.
C. Truesdell and W. Noll, The Non-Linear Field Theories of Mechanics, in S. Flügge (ed.), Handbuch der Physik, Vol III/3, Springer-Verlag, Berlin 1965.
C. C. Wang and C. Truesdell, Introduction to Rational Elasticity, Noordhoff, Leyden 1973.
Guo Z.-H., T. Lehmann, L. Haoyun, and C. Man, Twirl tensors and the equation AX — XA = C, J. Elasticity 27 (1992) 227–245.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Sansour, C. (1995). On Anisotropy at the Actual Configuration and the Adequate Formulation of a Free Energy Function. In: Parker, D.F., England, A.H. (eds) IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics. Solid Mechanics and Its Applications, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8494-4_6
Download citation
DOI: https://doi.org/10.1007/978-94-015-8494-4_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4589-8
Online ISBN: 978-94-015-8494-4
eBook Packages: Springer Book Archive