Abstract
Material symmetries of a continuum impose definite restrictions on the form of constitutive relations. The restrictions are specified in the representations of isotropic and anisotropic tensor functions and indicate the type and the number of independent variables involved in a constitutive relation. Thus, in a properly written constitutive equation, the material symmetries are automatically verified.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
WINEMAN, A.S. and PIPKIN, A.C., Material Symmetry Restrictions on Constitutive Equations, Arch. Rat. Mech. An., 17 (1964) : 184–214.
PIPKIN, A.C. and WINEMAN, A.S., Material Symmetry Restrictions on Non-Polynomial Constitutive Equations, Arch. Rat. Mech. An.,12 (1963) : 420–426.
SPENCER, A.J.M., Theory of Invariants, in Continuum Physics,ed. by C. Eringen, Academic Press, (1971) : 239–353.
WANG, C.C., On Representations for Isotropic Functions, Part I and II, Arch. Rat. Mech. An.,33 (1969) : 249-287.
WANG, C.C., A New Representation Theorem for Isotropic Functions, Part I and II, Arch. Rat. Mech. An.,36 (1970) : 166–223.
WANG, C.C.,Corrigendum, Arch. Rat. Mech. An.,43 (1971) : 392–395.
SMITH, G.F., On Isotropic Integrity Bases, Arch. Rat. Mech. An., 18 (1965) : 282–292.
SMITH, G.F., On a Fundamental Error in Two Papers of C.C. WANG, Arch. Rat. Mech. An.,36 (1970) : 161–165.
SMITH, G.F., On Isotropic Functions of Symmetric Tensors, Skew-Symmetric Tensors and Vectors, Int.J.Engng. Sci.,19 (1971) : 899–916.
RIVLIN, R.S. and ERICKSEN, J.L., Stress-Deformation Relations for Isotropic Materials, J. Rat. Mech. An.,4 (1955) : 323–425.
BOEHLER, J.P., On Irreducible Representations for Isotropic Scalar Functions, ZAMM,57 (1977) : 323–327.
BOEHLER, J.P.,Lois de Comportement Anisotrope des Milieux Continus, Journal de Mécanique,17,2 (1978) : 153–190.
BOEHLER, J.P., A Simple Derivation of Representations for Non-Polynomial Constitutive Equations in Some Cases of Anisotropy, ZAMM,59 (1979) : 157–167.
BOEHLER, J.P.,Functional Bases for Orthotropic and Transverse Isotropic Non-Polynomial Functions, (in preparation).
BOEHLER, J.P. and RACLIN, J.,Representations Irréductibles des Fonctions Tensorielles Anisotropes Non-Polynomiales de Deux Tenseurs Symétriques, Arch. Mech. Stos.,19,3 (1977) : 431–444.
ADKINS, J.E., Further Symmetry Relations for Transversely Isotropic Materials, Arch. Rat. Mech. An.,5 (1960) : 263–274.
ADKINS, J.E., Symmetry Relations for Orthotropic and Transversely Isotropic Materials, Arch. Rat. Mech. An.,4 (1960) : 193–213.
RIVLIN, R.S., Further Remarks on the Stress-Deformation Relations for Isotropic Materials, J. Rat. Mech. An.,4 (1955) : 681–702.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Wien
About this chapter
Cite this chapter
Boehler, J.P. (1987). Representations for Isotropic and Anisotropic Non-Polynomial Tensor Functions. In: Boehler, J.P. (eds) Applications of Tensor Functions in Solid Mechanics. International Centre for Mechanical Sciences, vol 292. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2810-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2810-7_3
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81975-3
Online ISBN: 978-3-7091-2810-7
eBook Packages: Springer Book Archive