A space fibre as added value in finite element modelling for optimal analysis of problems involving contact
DOI:
https://doi.org/10.13052/17797179.2012.702435Keywords:
special finite elements, contact, hyperelasticity, space fibre rotationAbstract
The present work deals with the non-linear formulation of an axisymmetric hyperelastic solid model, based on the concept space fibre rotation (SFR). The SFR-Axi model uses the kinematics of a space fibre to obtain a quite accurate displacement field. It improves in a significant way the precision of the linear element Q4-Axi. It can even be compared, on the accuracy and CPU time level, with the high-order elements as Q8-Axi for instance. A hyperelastic law, based on the Mooney–Rivlin model, is implemented to allow to the present model a better simulation of the forming process of hollow plastic bodies. The numerical results relate to primarily some known tests of hyperelastic structures, with and without contact (swellings).
Downloads
References
Ayad, R. (2002). Contribution to the numerical modeling for solid and structure analysis, and for non-
Newtonian fluid forming (HDR Thesis, University of Reims Champagne-Ardenne).
Crisfield, M.A. (1997). Non-linear finite element analysis of solids an structures (Vol. 2). England:
Wiley.
Ghomari, T. (2007). Contribution to 3D modeling of plastic bodies forming (PhD thesis, University of
Reims Champagne-Ardenne).
Heinstein, M.W., Mello, F.J., Attaway, S.W., & Laursen, T.A. (2000). Contact-impact modelling in
explicit transient dynamics. Computer Methods in Applied Mechanics and Engineering, 187, 621–
Hughes, T.J.R., & Carnoy, E. (1983). Nonlinear finite element shell formulation accounting for large
membrane strains. Computer Methods in Applied Mechanics and Engineering, 39, 69–82.
Mooney, M. (1940). A theory of large elastic deformation. Journal of Applied Physics, 6, 582–592.
Ogden, R.W. (1972). Large deformation isotropic elasticity-on the correlation of theory and experiment
for incompressible rubber like solids. Proceedings of the Royal Society of London, Series A: Mathematical
and Physical Sciences, 326, 565–584.
Rivlin, R.S. (1948). Large elastic deformation of isotropic materials. I. Fundamental concepts. Philosophical
Transactions of the Royal Society of London, 240, 459–490.
Sze, K.Y., Zhenga, S.J., Lob, S.H. (2004). A stabilized eighteen-node solid element for hyperelastic
analysis of shells. Finite Elements in Analysis and Design, 40, 319–340.
Treloar, L.R.G. (1976). The mechanics of rubber elasticity. Proceedings of the Royal Society of London,
, 301–330.
Wang, S., & Makinouchi, A. (2000). Contact search strategies for FEM simulation of the blow modelling
process. International Journal for Numerical Methods in Engineering, 48, 501–521.
Williams, J.G. (1970). A method of calculation for thermoforming plastics sheets. Journal of Strain
Analysis, 5(1), 49–57.
Zhong, Z.H., & Nilsson, L. (1994). Automatic contact searching for dynamic finite element analysis.
Computers & Structures, 52(2), 187–197.
Ziane, M. (1999). Contribution à la simulation numérique du soufflage thermoformage de corps creux
plastiques axisymétriques (Thèse de doctorat, Université de technologie de Compiègne).
Zouari, W., Ayad, A., Ben Zineb, T., & Benjeddou, A. (2012). A piezoelectric 3D hexahedral curvilinear
finite element based on the space fiber rotation concept. International Journal for Numerical Methods
in Engineering, 90(1), 87–115.
