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Structural Engineering and Mechanics Volume 21, Number 2, September30 2005 , pages 121-136 DOI: https://doi.org/10.12989/sem.2005.21.2.121 |
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A general convergence condition of the Newton-Raphson algorithm applied to compressible hyperelasticity |
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Francois Peyraut, Zhi-Qiang Feng and Nadia Labed
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| Abstract | ||
| This paper presents the implementation of the Blatz-Ko hyperelastic compressible model in a finite element program to deal with large deformation problems. We show analytically and numerically that the minimum number of increment steps in the Newton-Raphson algorithm depends on material properties and applied loads. We also show that this dependence is related to the orientation preservation principle. So we propose a convergence criteria based on the sign of eigenvalues of the deformation gradient matrix. | ||
| Key Words | ||
| Blatz-Ko model; hyperelasticity; finite element; large deformation; Newton-Raphson. | ||
| Address | ||
| Francois Peyraut; Laboratoire MŽcatronique3M, Universite de Technologie de Belfort-MontbŽliard, SŽvenans, 90010 Belfort cedex, France Zhi-Qiang Feng; Laboratoire de MŽcanique d?vry, Universite d?vry-Val d?ssonne,40, rue du Pelvoux, 91020 Evry cedex, France Nadia Labed; Laboratoire MŽcatronique3M, Universite de Technologie de Belfort-MontbŽliard,SŽvenans, 90010 Belfort cedex, France | ||