Preprint Article Version 1 This version is not peer-reviewed

# Dislocation Density Tensor of Thin Elastic Shells at Finite Deformation

Version 1 : Received: 29 June 2018 / Approved: 2 July 2018 / Online: 2 July 2018 (17:08:27 CEST)

How to cite: Sun, B. Dislocation Density Tensor of Thin Elastic Shells at Finite Deformation. Preprints 2018, 2018070018 (doi: 10.20944/preprints201807.0018.v1). Sun, B. Dislocation Density Tensor of Thin Elastic Shells at&nbsp;Finite Deformation. Preprints 2018, 2018070018 (doi: 10.20944/preprints201807.0018.v1).

## Abstract

The dislocation density tensors of thin elastic shells have been formulated explicitly in terms of the Riemann curvature tensor. The formulation reveals that the dislocation density of the shells is proportional to KA3=2, where K is the Gauss curvature and A is the determinant of metric tensor of the middle surface.

## Subject Areas

dislocation density tensor, thin shells, Riemann curvature tensor