Incompatible deformation field and Riemann curvature tensor

doi:10.1007/s10483-017-2176-8

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (3): 311-332.doi: https://doi.org/10.1007/s10483-017-2176-8

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Incompatible deformation field and Riemann curvature tensor

Bohua SUN

Department of Mechanical Engineering, Cape Peninsula University of Technology, Cape Town 7535, South Africa

收稿日期:2016-06-04 修回日期:2016-10-08 出版日期:2017-03-01 发布日期:2017-03-01
通讯作者: Bohua SUN, E-mail:sunb@cput.ac.za E-mail:sunb@cput.ac.za
基金资助:
Project supported by the National Research Foundation of South Africa (NRF) (No. 93918)

Incompatible deformation field and Riemann curvature tensor

Bohua SUN

Department of Mechanical Engineering, Cape Peninsula University of Technology, Cape Town 7535, South Africa

Received:2016-06-04 Revised:2016-10-08 Online:2017-03-01 Published:2017-03-01
Contact: Bohua SUN E-mail:sunb@cput.ac.za
Supported by:
Project supported by the National Research Foundation of South Africa (NRF) (No. 93918)

摘要/Abstract

摘要：

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 Kröner and Le-Stumpf are provided.

关键词: deformation gradient, dislocation density tensor, compatibility condition, Burgers vector, Riemann curvature tensor

Abstract:

Key words: Riemann curvature tensor, Burgers vector, dislocation density tensor, compatibility condition, deformation gradient

中图分类号:

Bohua SUN. Incompatible deformation field and Riemann curvature tensor[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 311-332.

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Incompatible deformation field and Riemann curvature tensor

Incompatible deformation field and Riemann curvature tensor

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