By J.P. Boehler

ISBN-10: 3211819754

ISBN-13: 9783211819753

ISBN-10: 3709128102

ISBN-13: 9783709128107

Contents: J.P. Boehler: actual motivation.- J.P. Boehler: creation to the invariant formula of anisotropic constitutive equations.- J.P. Boehler: Representations for isotropic and anisotropic non-polynomial tensor functions.- J.P. Boehler: Anisotropic linear elasticity.- J.P. Boehler: Yielding and failure of transversely isotropic solids.- J.P. Boehler: On a rational formula of isotropic and anisotropic hardening.- J.P. Boehler: Anisotropic hardening of rolled sheet-steel.- A.J.M. Spencer: Isotropic polynomial invariants and tensor functions.- A.J.M. Spencer: Anisotropic invariants and extra effects for invariant and tensor representations.- A.J.M. Spencer: Kinematic constraints, constitutive equations and failure principles for anisotropic materials.- J. Betten: Invariants of fourth-order tensors.- J. Betten: formula of anisotropic constitutive equations.- J. Betten: Interpolation equipment for tensor functions.- J. Betten: Tensor functionality idea and classical plastic strength.

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Extra info for Applications of Tensor Functions in Solid Mechanics

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TrM A. trM A. trM A. trM A. • -33-1 -22-1 -11-1 -12-1 -31-1 -23-1 (21) The analysis of the explicit expressions show that the invariants (21) are just the independent components in the (v , v , v ) frame of the agen(") cies A. : trMk 0 A. "' -2 -1 -3 . Any scalar invariant of the A. can be expressed -1 uniquely with respect to the invariants (21). Thus, the invariants (21) constitute a complete functional basis. As they are functionally independent, this functional basis is irreducible a fortiori.

18 (1965) : 282-292. Representations for Tensor Functions 53 8. C. WANG, Arch. Rat. Mech. , 36 (1970) : 161-165. 9. Engng. , 19 (1971) : 899-916. S. , Stress-Deformation Relations for Isotropie Materials, J. Rat. Mech. , 4 (1955) : 323-425. , On Irreducihle Representations for Isotropie Scalar Functions, ZAMM, 57 (1977) : 323-327. ,Lois de Comportement Anisotrope des Milieux Continus, Journal de Mecanique, 17,2 (1978) : 153-190. , A Simple Derivation of Representations for NonPolynomial Constitutive Equations in Some Cases of Anisotropy, ZAMM, 59 (1979) : 157-167.

11) whereas in the general non-polynomial case, the irreducible generating set contains the eight tensors {9), the last generator (11)being then redundant. Consider the list of an arbitrary nurnber of symmetric second order tensors: A , A -l -2 ••. P. Boehler 40 The integrity basis for the list (12) contains the traces of products of up to six tensors [7], whereas the functional basis contains the traces only up to the order three (Table I). Similarly, the generating set in the polynomial case contains products of up to five tensors [31, whereas in the general case, it contains products up to only two tensors (Table II).

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Applications of Tensor Functions in Solid Mechanics by J.P. Boehler

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