Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials

We present formulations for compressible and incompressible hyperelastic thin shells which can use general 3D constitutive models. The necessary plane stress condition is enforced analytically for incompressible materials and iteratively for compressible materials. The thickness stretch is staticall...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2015-07, Vol.291 (C), p.280-303
Main Authors: Kiendl, Josef, Hsu, Ming-Chen, Wu, Michael C.H., Reali, Alessandro
Format: Article
Language:English
Subjects:
Compressibility
Computer simulation
Construction
Discretization
Finite strain
Hyperelastic
Incompressibility
Isogeometric
Kirchhoff–Love
Mathematical analysis
Mathematical models
Thin shell
Thin walled shells
Three dimensional models
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Summary:We present formulations for compressible and incompressible hyperelastic thin shells which can use general 3D constitutive models. The necessary plane stress condition is enforced analytically for incompressible materials and iteratively for compressible materials. The thickness stretch is statically condensed and the shell kinematics are completely described by the first and second fundamental forms of the midsurface. We use C1-continuous isogeometric discretizations to build the numerical models. Numerical tests, including structural dynamics simulations of a bioprosthetic heart valve, show the good performance and applicability of the presented methods.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2015.03.010