Applied Mathematics and Mechanics (English Edition)
题名：Incompatible deformation field and Riemann curvature tensor
作者：Bohua SUN
单位：Department of Mechanical Engineering, Cape Peninsula University of Technology, Cape Town 7535, South Africa
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：compatibility condition   Riemann curvature tensor   deformation gradient   Burgers vector   dislocation density tensor
全文链接：http://www.amm.shu.edu.cn/EN/abstract/abstract15034.shtml