Finite bending of a multilayered cylindrical nanosector with residual deformations

Abstract

This paper deals with the universal model describing plane strain bending of a multilayered sector of a cylindrical tube which can have residual deformations as well as nano-scale effects. In order to model the response of the sector at the nano-scale, the Gurtin–Murdoch theory is employed. Residual deformations of the layers, such as prestretch or precompression, are introduced into the model of finite bending using the multiplicative decomposition rule for corresponding deformation gradients. Numerous coupled nonlinear effects exhibited by the sector are discussed.