Modelisation dynamique du thermoformage
Keywords:
thermoforming, finite elements method, membrane, hypere/asticily, nonlinear viscoelasticity, dynamic explicit scheme, mesh refinementAbstract
A numerical software was developed ta simulate the thermoforming process. The numerical model is based on a total Lagrangian finite element method and the equation of motion is integrated via an explicit scheme. The heat-softened polymer sheets are modeled by hyperelastic or non-linear viscoelastic incompressible membranes, the usual assomption of sticking contact is adopted and an adaptative mesh refinement scheme was implemented. The finite element results are compared with semi-analytical and exprimental results and successful calculations are made using a critical mold geometry.
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References
[CHA 76] CHANG W. V., BLOCH R., TSCHOEGL N. W., «On the theory of the viscoelastic
behavior of soft polymers in moderately large deformations», Rheol. Acta, 15, 1976,
p. 367-378.
[CHR 80] CHRISTENSEN R. M ., «A nonlinear theory of viscoelas ti city for application to
elastomers», J. Appl. Mech. ASME, 47, 1980, p. 762-768.
[DEL 9 1] DELORENZI H. G., NIED H. F.,« Finite element simulation of thermoforming and
blow molding>>, Progress in Polymer Processing. Hanser Verlag, (1991 ), p. 117- 171 .
[DOK 89] DOKA!NISH M . A ., SUDDARAJ K ., «A survey of direct time-integration methods
in computational structural dynamics. I. Explicit methods>>, Comput. Stmct., 32, 1989,
p. 1371 -1386.
[FEN 861 FENG W. W., «A recurrence formula for viscoelastic constitutive equations>>, Proceedings
of the International Conference 0 11 Computational Mechanics vol. IV, ( 1986),
p. 77-8 1.
[KHA 92] KHAYAT R. E., DERDOURt A ., GAR t A-R~JON A .,« In nation of an clastic cy lindrical
membrane: non-linear defonnation and instability >>, In t. J. Solids Structu res, 29,
p. 69-87.
[MOO 401 MOONEY M ., «A theory of large clastic deformation >>, J. Appl. Phys., II , 1940,
p. 582-592.
LNAM 93] NAMDtAR R. V., VALERA R. S., LAWRENCE K. L ., MORGAN R. B .. AMtL D.,
« An algorithm for adaptati ve refi nement oftriangular element meshe >> . Int. J. Num. Meth.
Eng., 36, 1993, p. 499-509.
[OGD 72] OGDEN R. W., « Large deformation isotropic elasticity - on the correlation of theory
and experiment for incomprc sible rubberlike solids>>, Proc. R. Soc. Lond. , A326, 1972,
p. 565-584.
[RA 94) RA HIK M ., ROELANDT J. M ., BATOZ J. L ., « Simulati on numcrique du so uffiage
et du thermoformage des plas tiques», Revue europeenne des elemen ts finis, 3, 1994, p.
-2 10.
[SCH 75] SCHMIDT L. R., CARLEY J. F.,« Biaxial stretching of heat-softened pl astic sheets:
experiments and results>>, Polym. Eng. Sci., 15, 1975, p. 51-62.
[VER 97] V ERRON E., «Contribution experimentale et numcrique aux proecdcs de moulage
par soufnage et de thermoformage >>, These de doctoral, Ecole Centrale de Nantes, 1997.
[WAR 83] WARD I. M ., Meclzanical properties of solid polymers, second edi tion, John Wiley
and Sons Ltd, 1983.
[ZAM 89] ZAMAN! N. G., WATT 0. F., ESTEGHAMATIAN M ., «Status of the finite element
method in the thermoforming process», Int. J. Num. Meth. Eng., 28, 1989, p. 268 1-2693.
(ZIE 94) ZIEN KIEWIECZ 0 . C., TAYLOR R. L., The finite element method. Volume 1: Basic
formulation and linear problems, fourth edition, MacGraw-Hill ompany, 1994.
