Generic separating sets for three-dimensional elasticity tensors. (28th June 2019)

• Record Type: Journal Article
• Authors: Desmorat, R.; Auffray, N.; Desmorat, B.; Kolev, B.; Olive, M.
• Is Part Of: Proceedings. Volume 475:Number 2226(2019)
• Publication Date: 2019-06-28
• Subjects: anisotropy -- polynomial invariants -- rational invariants -- separating sets; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2019.0056
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : We define a generic separating set of invariant functions (a.k.a. a weak functional basis ) for tensors. We then produce two generic separating sets of polynomial invariants for three-dimensional elasticity tensors, one consisting of 19 polynomials and one consisting of 21 polynomials (but easier to compute), and a generic separating set of 18 rational invariants. As a by-product, a new integrity basis for the fourth-order harmonic tensor is provided.