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Title: Incompatible deformation field and Riemann curvature tensor
Authors: Sun, BoHua 
Keywords: Compatibility condition;Riemann curvature tensor;Deformation gradient;Burgers vector dislocation density tensor
Issue Date: 2017
Publisher: Springer
Abstract: Compatibility conditions of a deformation field in continuum mechanics have been revisited via two different routes. One is to use the deformation gradient, and the other is a pure geometric one. Variations of the displacement vector and the displacement density tensor are obtained explicitly in terms of the Riemannian curvature tensor. The explicit relations reconfirm that the compatibility condition is equivalent to the vanishing of the Riemann curvature tensor and reveals the non-Euclidean nature of the space in which the dislocated continuum is imbedded. Comparisons with the theory of Kr¨oner and Le-Stumpf are provided.
ISSN: 0253-4827
Appears in Collections:Eng - Journal articles (DHET subsidised)

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