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

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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 Sead 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. In order to preserve the basic features of a displacement formulation the extra strain term is incorporated via the enhanced assumed strain concept recently proposed by Simo and Rifai to improve the performance of finite elements. Since the extra strain parameter can be eliminated on the element level after discretization, the formulation preserves the formal structure of a 6‐parameter shell theory. The resulting hybrid‐mixed shell formulation is applied to large deformation problems with hyperelasticity, small and large strain plasticity.

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