Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept

TLDR: In this article, a 7-parameter theory with a linear varying thickness stretch as an extra variable allowing also large strain effects is presented, and the authors introduce a complete 3-D constitutive law without modification.

Abstract: Conventional shell formulations, such as 3- or 5-parameter theories or even 6-parameter theories including the thickness change as extra parameter, require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness. This means that the normal stress in thickness direction has to either vanish or be constant. In general, these extra constraints cannot be satisfied explicitly or they lead to elaborate strain expressions. The main objective of the present study is to introduce directly a complete 3-D constitutive law without modification. Therefore, a 7-parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects