Préservation de l’orientation et convergence de Newton-Raphson avec le modèle hyperélastique compressible de Blatz-Ko
Keywords:
compressible hyperelasticity, Blatz-Ko model, incremental Newton-Raphson, arc length method, orientation preservationAbstract
This paper deals with the Blatz-Ko hyperelastic compressible model in the case of a cubic structure under compression loading by a press. With some particular increment loading values, we show that the orientation is not preserved. In this case, the incremental Newton-Raphson algorithm diverges. With the arc length method, we obtain a similar conclusion for some arc length values. So we suggest to control the convergence by using optimal numerical parameters. These optimal numerical parameters guarantee the orientation preservation and a minimal time computation.
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References
[ARO 98] ARON M., CHRISTOPHER C., WANG Y., « On the Straightening of Compressible,
Nonlinearly Elastic, Annular Cylindrical Sectors », Mathematics and Mechanics of
Solids, Vol. 3, p. 131-145, 1998.
[BLA 62] BLATZ P.J. , KO W.L., « Application of Finite Elastic Theory to the Deformation of
Rubbery Materials », Transactions of the Society of Rheology, Vol. 6, p. 223-251, 1962.
[CIA 85] CIARLET P.G., Elasticité Tridimensionnelle, Masson, Collection RMA, 1985.
[FOR 87] FORDE W.R.B., STIEMER S.F., « Improved Arc Length Orthogonality Methods for
Nonlinear Finite Element Analysis », Computer & Structures, Vol. 27, No. 5, p. 625-630,
[HOR 95] HORGAN C.O., POLIGNONE D.A., « A Note on the Pure Torsion of a Circular
Cylinder for a Compressible Nonlinearly Elastic Material with Nonconvex Strainenergy
», Journal of Elasticity, Vol. 37, p. 167-178, 1995.
[HOR 96] HORGAN C.O., « Remarks on Ellipticity for the Generalized Blatz-Ko Constitutive
Model for a Compressible Nonlinearly Elastic Solid », Journal of Elasticity, Vol. 42,
p. 165-176, 1996.
[WIN 95] WINEMAN A.S., WALDRON JR W.K., « Normal Stress Effects Induced during Circular
Shear of a Compressible Non-Linear Elastic Cylinder », Int. J. Non-Linear Mechanics,
Vol. 30, No. 3, p. 323-339, 1995.
