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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