Irreducible decompositions of physical tensors of high orders. (English) Zbl 0969.74009

Zheng, Q.-S.; Zou, W.-N.

J. Eng. Math. 37, No. 1-3, 273-288 (2000).

Summary: We use the term ‘physical tensor’ for a tensor that belongs to a tensor subspace. Based on the relationship among the characters of rotation representation, some techniques are developed in order to give the numbers of independent deviatoric tensors contained in irreducible decompositions of physical tensors, even prior to the constructions of irreducible decompositions. Some examples are shown, and many of them are new results.

MSC:

74A99	Generalities, axiomatics, foundations of continuum mechanics of solids
74B99	Elastic materials
15A72	Vector and tensor algebra, theory of invariants

Keywords:

physical tensor; deviatoric tensors; high-order tensors; elasticity; tensor subspace; rotation representation; irreducible decompositions