A minimal integrity basis for the elasticity tensor. (English) Zbl 1372.74013
Summary: We definitively solve the old problem of finding a minimal integrity basis of polynomial invariants of the fourth-order elasticity tensor \(\mathbf{C}\). Decomposing \(\mathbf{C}\) into its \(\mathrm{SO}(3)\)-irreducible components we reduce this problem to finding joint invariants of a triplet \((\mathbf{a}, \mathbf{b}, \mathbf{D})\), where \(\mathbf{a}\) and \(\mathbf{b}\) are second-order harmonic tensors, and \(\mathbf{D}\) is a fourth-order harmonic tensor. Combining theorems of classical invariant theory and formal computations, a minimal integrity basis of 297 polynomial invariants for the elasticity tensor is obtained for the first time.
MSC:
| 74B10 | Linear elasticity with initial stresses |
| 11D04 | Linear Diophantine equations |
| 15A72 | Vector and tensor algebra, theory of invariants |
Software:
NormalizReferences:
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