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Two-dimensional Hooke’s tensors – Isotropic decomposition, effective symmetry criteria. (English) Zbl 0848.73010

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.

MSC:

74B05 Classical linear elasticity
15A72 Vector and tensor algebra, theory of invariants
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