Integrity basis for a second‐order and a fourth‐order tensor | Zendy

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Integrity basis for a second‐order and a fourth‐order tensor

Author(s) -

Josef Betten

Publication year - 1982

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/s0161171282000088

Subject(s) - mathematics , tensor contraction , cartesian tensor , tensor (intrinsic definition) , symmetric tensor , order (exchange) , scalar (mathematics) , tensor density , cauchy elastic material , isotropy , tensor product of hilbert spaces , basis (linear algebra) , tensor field , pure mathematics , tensor product , mathematical analysis , exact solutions in general relativity , constitutive equation , geometry , physics , finite element method , finance , quantum mechanics , economics , thermodynamics

In this paper a scalar-valued isotropic tensor function is considered, the variables of which are constitutive tensors of orders two and four, for instance, characterizing the anisotropic properties of a material. Therefore, the system of irreducible invariants of a fourth-order tensor is constructed. Furthermore, the joint or simultaneous invariants of a second-order and a fourth-order tensor are found. In a similar way one can construct an integrity basis for a tensor of order greater than four, as shown in the paper, for instance, for a tensor of order six

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