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Polyconvex energy densities with applications to anisotropic thin shells
Author(s) -
Balzani D.,
Schröder J.,
Gruttmann F.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700437
Subject(s) - transverse isotropy , isotropy , anisotropy , superposition principle , strain energy , focus (optics) , strain energy density function , work (physics) , constitutive equation , matrix (chemical analysis) , mathematical analysis , mathematics , classical mechanics , materials science , physics , finite element method , composite material , optics , thermodynamics
This work shows the capability to simulate anisotropic thin shells using polyconvex energy densities by analyzing numerical examples. The variational framework is based on the enhanced assumed strain formulation. The iterative enforcement of the zero normal stress condition at the integration points allows consideration of arbitrary three–dimensional constitutive equations. We consider an additive structure of the energy decoupled in an isotropic part for a matrix material and the superposition of transversely isotropic parts for embedded fiber families and focus on polyconvex strain energy functions. In two representative examples we document anisotropy effects. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)