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

• Main Author: Josef Betten
• Format: Article
• Language: English
• Published: Hindawi Limited 1982-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Subjects: theory of algebraic invariants; integrity basis under a subgroup; isotropic tensor functions; representation-theory; irreducible basic and principal invariants of a fourth-order tensor; constitutive tensors; characteristic polynomial; alternation process; integrity basis for a tensor of order greater than four; bilinear operator; construction of simultaneous or joint invariants; Hamilton-Cayley's theorem; isotropic constitutive tensors.
• Online Access: http://dx.doi.org/10.1155/S0161171282000088

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.