Structural Engineering and Mechanics

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A general convergence condition of the Newton-Raphson algorithm applied to compressible hyperelasticity

  • Peyraut, Francois (Laboratoire Mecatronique3M, Universite de Technologie de Belfort-Montbeliard) ;
  • Feng, Zhi-Qiang (Laboratoire de Mecanique d'Evry, Universite d'Evry-Val d'Essonne) ;
  • Labed, Nadia (Laboratoire Mecatronique3M, Universite de Technologie de Belfort-Montbeliard)
  • Received : 2004.12.08
  • Accepted : 2005.06.21
  • Published : 2005.09.30
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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.

Keywords

References

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