International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 1, Pages 87-96
doi:10.1155/S0161171282000088

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

Josef Betten

Rheinisch-Westfälische Technische Hochschule Aachen, Templergraben 55, Aachen D-5100, Germany

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.