Implémentation éléments finis d’une condition optimale de préservation de l’orientation
Cas du contact en grandes déformations hyperélastiques
Keywords:
orientation preservation, compressible hyperelasticity, Blatz-Ko model, contact mechanicsAbstract
For the Blatz-Ko compressible hyperelastic model, an orientation preservation defect leads to the divergence of the Newton-Raphson algorithm. It is thus important to find a criterion in order to detect such a defect during a numerical calculation. In this paper, we propose a criterion based on the change of sign of the deformation gradient matrix eigenvalues between the deformed and undeformed configurations. It is shown that this criterion does not depend on the geometry and the loading and that it allows an optimal convergence. Its implementation in a finite element software is presented. Finally, this criterion is validated on several examples. One of these examples deals with the contact problem between two deformable hyperelastic bodies.
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