Incompatible deformation field and Riemann curvature tensor

作者：Sun Bohua^*

来源：Applied Mathematics and Mechanics (English Edition ), 2017, 38(3): 311-332.

DOI：10.1007/s10483-017-2176-8

• compatibility condition
• Riemann curvature tensor
• deformation gradient
• Burgers vector
• dislocation density tensor

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 KrAoner and Le-Stumpf are provided.

• 出版日期2017-3