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: advent 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 conception and classical plastic capability.

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Extra resources for Applications of Tensor Functions in Solid Mechanics

Example text

As the tensors (18) are linearly independent, this generatingset is irreducible. Finally, an irreducible representation for the general anisotropic is given by: tensor function F of the agencies A. -1 ~ M T 1-11 + u M 2-22 + u M 3-33 + u (M 4 -23 ) + + M -32 (22) ~. ) -12-1 i=1,2, ... a. This result could have been established directly. Indeed, the tensor T can always be expressed as a linear combination of the basic tensors (18), with the components Tmn of T as coefficients. P. ~±I- s where S , S , S -1 -3 -2 , S , S , S l (23) -3~ -2 -1 are the reflections with respect to the basic planes (v , v ), (v , v ), (v , v ) of the orthonormal privileged frame -l -1 -3 -3 -2 -2 (v , V , V ).

Finally, an irreducible representation for the general anisotropic is given by: tensor function F of the agencies A. -1 ~ M T 1-11 + u M 2-22 + u M 3-33 + u (M 4 -23 ) + + M -32 (22) ~. ) -12-1 i=1,2, ... a. This result could have been established directly. Indeed, the tensor T can always be expressed as a linear combination of the basic tensors (18), with the components Tmn of T as coefficients. P. ~±I- s where S , S , S -1 -3 -2 , S , S , S l (23) -3~ -2 -1 are the reflections with respect to the basic planes (v , v ), (v , v ), (v , v ) of the orthonormal privileged frame -l -1 -3 -3 -2 -2 (v , V , V ).

1 -2 -3 Consider the three tensors: M -1 V -1 ~ = M -2 V -1 M V ~ V -2 -2 V -3 -3 ~ V -3 (24) The expressions of the tensors (24) are given by (19). It is easy to show that the group ( 23) is the invariance group of the tensors ( 24) : = M. Qt -1 --1- QE S 1,2,3 . i (25) Thus, the tensors (24) are the structural tensors for orthotropy. The representation for the isotropic function T = F(A, ... A, M , M, M) - - -1 -a -1 -2 (26) -3 obtained from Table I and II, is a complete representation for F considerBut the ed as a general orthotropic function of the agencies A , ...

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