Integrity basis for a second-order and a fourth-order tensor
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 constructe...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1982-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171282000088 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832565104565026816 |
|---|---|
| author | Josef Betten |
| author_facet | Josef Betten |
| author_sort | Josef Betten |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-64c6ae85048d422ea649bcae59a4bac1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-64c6ae85048d422ea649bcae59a4bac12025-02-03T01:09:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-0151879610.1155/S0161171282000088Integrity basis for a second-order and a fourth-order tensorJosef Betten0Rheinisch-Westfälische Technische Hochschule Aachen, Templergraben 55, Aachen D-5100, GermanyIn 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.http://dx.doi.org/10.1155/S0161171282000088theory of algebraic invariantsintegrity basis under a subgroupisotropic tensor functionsrepresentation-theoryirreducible basic and principal invariants of a fourth-order tensorconstitutive tensorscharacteristic polynomialalternation processintegrity basis for a tensor of order greater than fourbilinear operatorconstruction of simultaneous or joint invariantsHamilton-Cayley's theoremisotropic constitutive tensors. |
| spellingShingle | Josef Betten Integrity basis for a second-order and a fourth-order tensor International Journal of Mathematics and Mathematical Sciences 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. |
| title | Integrity basis for a second-order and a fourth-order tensor |
| title_full | Integrity basis for a second-order and a fourth-order tensor |
| title_fullStr | Integrity basis for a second-order and a fourth-order tensor |
| title_full_unstemmed | Integrity basis for a second-order and a fourth-order tensor |
| title_short | Integrity basis for a second-order and a fourth-order tensor |
| title_sort | integrity basis for a second order and a fourth order tensor |
| topic | 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. |
| url | http://dx.doi.org/10.1155/S0161171282000088 |
| work_keys_str_mv | AT josefbetten integritybasisforasecondorderandafourthordertensor |