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Extension of the ‘solid‐shell’ concept for application to large elastic and large elastoplastic deformations
Author(s) -
Hauptmann R.,
Schweizerhof K.,
Doll S.
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/1097-0207(20001130)49:9<1121::aid-nme130>3.0.co;2-f
Subject(s) - plasticity , shell (structure) , displacement (psychology) , degrees of freedom (physics and chemistry) , deformation (meteorology) , tensor (intrinsic definition) , mechanics , finite element method , mathematics , classical mechanics , structural engineering , geometry , materials science , physics , engineering , mechanical engineering , psychology , quantum mechanics , psychotherapist , composite material
Abstract In the present contribution we extend a previously proposed so‐called solid–shell concept which incorporates only displacement degrees of freedom to the simulation of large elastic and large elastoplastic deformations of shells. Therefore, the modifications necessary for hyper‐elastic or elastoplastic material laws are discussed. These modifications concern the right Cauchy–Green tensor for large elastic deformations, respectively, the deformation gradient for elastoplasticity which then are consistent to the modified Green–Lagrange strains that are necessary for transverse shear and membrane locking free solid–shell element formulations. However, in addition to the locking mentioned above especially in the range of plasticity incompressibility locking becomes important. Thus, the second major aspect of this contribution is the discussion of several ways to avoid incompressibility locking also including the investigation of eigenmodes. Finally, a selective reduced integration scheme with reduced integration for the volumetric term is employed and described in detail, although it is limited to material laws which allow the decomposition into a volumetric and a deviatoric part. Some numerical examples show the range of application for the proposed elements. Copyright © 2000 John Wiley & Sons, Ltd.