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

Francois Peyraut , Zhi-Qiang Feng , Nadia Labed

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, FranceZhi-Qiang Feng; Laboratoire de MŽcanique d?vry, Universite d?vry-Val d?ssonne,40, rue du Pelvoux, 91020 Evry cedex, FranceNadia Labed; Laboratoire MŽcatronique3M, Universite de Technologie de Belfort-MontbŽliard,SŽvenans, 90010 Belfort cedex, France

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