Structure of tensor fields of the second rank generated by an incompatibility operator
type: Item
instance of: scholarly article
title: Structure of tensor fields of the second rank generated by an incompatibility operator
zbMATH Open document ID: 0538.73003
DOI: 10.1016/0021-8928(82)90068-5
author: S. E. Bugaenko
published in: Journal of Applied Mathematics and Mechanics
publication date: 1983-01-01T00:00:00Z
review text: The author is concerned with the structure of symmetric tensors of the second rank, generated by Kröner's incompatibility operator (i.e., \(I_{nk}\eta =\nabla \times \eta \times \nabla)\) [\textit{E. Kröner}, Continuum theory of dislocations and eigenstresses (1958; Zbl 0084.400)]. It is shown that the tensor is uniquely decomposed into the deviator and spherical parts, and it is proved that every piecewise continuously differentiable tensor field can be decomposed into an incompatible deviator and a compatible part.
Mathematics Subject Classification ID: 74Axx
Mathematics Subject Classification ID: 53A45
Mathematics Subject Classification ID: 53B50
zbMATH DE Number: 3856484
zbMATH Keywords: structure of symmetric tensors
zbMATH Keywords: second rank
zbMATH Keywords: Kröner's incompatibility operator
zbMATH Keywords: uniquely decomposed into the deviator and spherical parts
zbMATH Keywords: piecewise continuously differentiable tensor field
zbMATH Keywords: decomposed into an incompatible deviator and a compatible part
reviewed by: Sitiro Minagawa
MaRDI profile type: Publication
full work available at URL: 0021-8928(82)90068-5
OpenAlex ID: W2019027081
cites work: Q3253075
cites work: Q5342351
cites work: Q4743816
cites work: Q3847171
cites work: Q3293909
cites work: Problems with additional strains and modeling of them
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description: scientific article; zbMATH DE number 3856484