Blinowski, A.; Ostrowska-Maciejewska, J.; Rychlewski, J. Two-dimensional Hooke’s tensors – Isotropic decomposition, effective symmetry criteria. (English) Zbl 0848.73010 Arch. Mech. 48, No. 2, 325-345 (1996). Summary: Any fourth rank plane tensor \(H\) obeying the “Hooke’s” symmetries \(H_{ijkl}= H_{jikl}= H_{klij})\) can be split into three parts, behaving differently under the two-dimensional space rotation and belonging to the three different, mutually orthogonal, two-dimensional subspaces remaining invariant under the rotation. Such representation leads to a convenient set of functionally independent invariants, vanishing of some of these invariants demarcating the transitions of the tensor to the higher symmetry class. A nontrivial effective condition for orthotropy has been obtained. Some problems concerning the necessary and complete set of measurements of the elastic properties are also encountered. Cited in 9 Documents MSC: 74B05 Classical linear elasticity 15A72 Vector and tensor algebra, theory of invariants Keywords:fourth rank plane tensor; functionally independent invariants; condition for orthotropy PDFBibTeX XMLCite \textit{A. Blinowski} et al., Arch. Mech. 48, No. 2, 325--345 (1996; Zbl 0848.73010)