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On the integrability of second-order \(G\)-structures with applications to continuous theorems of dislocations. (English) Zbl 0811.53023

Summary: The material structure of a uniform elastic body whose mechanical response is sensitive to both the first and second gradients of the deformation is shown to be closely mirrored by the geometric notion of second-order \(G\)-structures. The presence of inhomogeneities, such as dislocations and disclinations, manifests itself through the lack of integrability of the associated \(G\)-structure. A measure of second-order inhomogeneity is introduced and condition of integrability are derived for important particular structure groups.

MSC:

53C10 \(G\)-structures
74B99 Elastic materials
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