Instabilité et bifurcation du soufflage de membranes hyperélastiques
Keywords:
membranes, hyperelasticity, inflation, instability, bifurcationAbstract
This article deals with the post-bifurcating behaviour of inflated hyperelastic membranes. Axisymmetrical and three dimensional formulations are studied. In both cases, the resulting algebraic system is solved by the combining classical Newton-Raphson scheme and the arc-length continuation method. The emphasize is laid on singular points and secondary paths are pointed out. Finally, numerical examples are considered in order to illustrate the developments.
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References
[ALE 71] ALEXANDER H., « The tensile instability of initially spherical balloons », Int. J.
Engng Sci., vol. 9, 1971, p. 151-162.
[BAT 79] BATOZ J. L., DHATT G., « Incremental displacement algorithms for nonlinear problems
», Int. J. Num. Meth. Engng, vol. 14, 1979, p. 1262-1267.
[BEA 87] BEATTY M. F., « Topics in finite elasticity : hyperelasticity of rubber, elastomers,
and biological tissues - with examples », Appl. Mech. Rev., vol. 40, n 12, 1987, p. 1699-
[CHA 87] CHARRIER J. M., SHRIVASTAVA S., WU R., « Free and constrained inflation of
elastic membranes in relation to thermoforming - Axisymmetric problems », J. Strain Analysis,
vol. 22, n 2, 1987, p. 115-125.
[DUF 86] DUFFET G. A., REDDY B. D., « The solution of multi-parameter systems of equations
with application to problems in nonlinear elasticity », Comp. Meth. Appl. Mech.
Engng, vol. 59, 1986, p. 179-213.
[GRE 60] GREEN A. E., ADKINS J. E., Large elastic deformations, The Clarendon Press,
Oxford, 1960.
[HAU 80] HAUGHTON D. M., « Post-bifurcation of perfect and imperfect spherical elastic
membranes », Int. J. Solids Structures, vol. 16, 1980, p. 1123-1133.
[HSU 94] HSU F. P. K., SCHWAB C., RIGAMONTI D., HUMPHREY J. D., « Identification of
response functions from axisymmetric membrane inflation tests : implications for biomechanics
», Int. J. Solids Struct., vol. 31, n 24, 1994, p. 3375-3386.
[KHA 92] KHAYAT R. E., DERDOURI A., GARCIA-RÉJON A., « Inflation of an elastic cylindrical
membrane : non-linear deformation and instability », Int. J. Solids Structures,
vol. 29, n 1, 1992, p. 69-87.
[KHA 94] KHAYAT R. E., DERDOURI A., « Inflation of hyperelastic cylindrical membranes
as applied to blow moulding. part I. axisymmetric case », Int. J. Num. Meth. Eng., vol. 37,
, p. 3773-3791.
[KYR 91] KYRIAKIDES S., CHANG Y., « The initiation and propagation of a localized instability
in an inflated elastic tube », Int. J. Solids Struct., vol. 27, n 9, 1991, p. 1085-1111.
[MAR 01] MARCKMANN G., VERRON E., PESEUX B., « Finite element analysis of blow
molding and thermoforming using a dynamic explicit procedure », Polym. Eng. Sci.,
vol. 41, n 3, 2001, p. 426-439.
[NEE 77] NEEDLEMAN A., « Inflation of spherical rubber balloons », Int. J. Solids Structures,
vol. 13, 1977, p. 409-421.
[REE 95] REESE S., WRIGGERS P., « A finite element method for stability problems in finite
elasticity », Int. J. Num. Meth. Eng., vol. 38, 1995, p. 1171-1200.
[SHI 96] SHI J.,MOITA G. F., « The post-critical analysis of axisymmetric hyper-elastic membranes
by the finite element method », Comput. Methods Appl. Mech. Engng, vol. 135,
, p. 265-281.
[SOK 97] SOKÓL T., WITKOWSKI M., « Some experiences in the equilibrium path determination
», Comput. Assist. Mech. Engng Sci., vol. 4, 1997, p. 189-208.
[VER 99] VERRON E., KHAYAT R. E., A. A. D., PESEUX B., « Dynamic inflation of hyperelastic
spherical membranes », J. Rheol., vol. 43, n 5, 1999, p. 1083-1097.
[VER 01a] VERRON E., MARCKMANN G., « An axisymmetric B-spline model for the nonlinear
inflation of rubberlike membranes », Comput. Meth. Appl. Mech. Engng, vol. 190,
n 46-47, 2001, p. 6271-6289.
[VER 01b] VERRON E., MARCKMANN G., PESEUX B., « Dynamic inflation of non-linear
elastic and viscoelastic rubberlike membranes », Int. J. Num. Meth. Engng, vol. 50, n 5,
, p. 1233-1251.
[YAN 70] YANG W. H., FENG W. W., « On axisymmetrical deformations of nonlinear membranes
», J. Appl. Mech. ASME, vol. 37, 1970, p. 1002-1011.
