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

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  • Josef Betten

Abstract

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.

Suggested Citation

  • Josef Betten, 1982. "Integrity basis for a second-order and a fourth-order tensor," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 5, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:354081
    DOI: 10.1155/S0161171282000088
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