Finite element formulation of the Ogden material model with application to ruber-like shells

International Journal for Numerical Methods in Engineering

Volumn 42, Issue 7, 1998, Pages 1279-1305

  Başar, Yavuz ^a   Itskov, Mikhail ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Finite elements; Incompressibility; Large elastic strains and finite rotations; Ogden model; Shell structures

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; KINEMATICS; MATHEMATICAL MODELS; ROTATION; RUBBER PRODUCTS; STRAIN;

ELASTIC STRAINS;

SHELLS (STRUCTURES);

EID: 0032137046     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19980815)42:7<1279::AID-NME437>3.0.CO;2-I     Document Type: Article

References (31)

1. H. Parisch, 'Efficient non-linear finite element shell formulation involving large strains,' Engng. Comput., 3, 121-128, 1986.
2. J.C. Simo, M.S. Rifai and D.D. Fox, 'On a stress resultant geometrically exact shell model. Part IV: variable thickness with through-the-thickness stretching,' Comput. Meth. Appl. Mech. Engng., 81, 91-126, 1990.
3. A. Kühlhorn and H. Schoop, 'A nonlinear theory of sandwich shells including the wrinkling phenomenon', Arch. Appl. Mech., 62, 413-427, 1992.
4. N. Büchter, E. Ramm and D. Roehl, 'Three-dimensional extension of nonlinear shell formulation based on the enhanced assumed strain concept', Int. J. Numer. Meth. Engng., 37, 2551-2568, 1994.
5. nd Biennial Eur. Joint Con. on Engineering Systems, Design and Analysis, Queen Mary and Westfield College, University of London, July 4-7, 1994.
6. C. Sansour, 'A theory and finite element formulation of shells at finite deformations involving thickness change: circumventing the use of a rotation tensor,' Arch. Appl. Mech., 65, 194-216, 1995.
7. P. Betsch, 'Statische und dynamische Berechnungen von Schalen endlicher elastischer Deformationen mit gemischten Finiten Elementen', Dissertation, Universität Hannover, 1996.
8. B. Schieck, W. Pietraszkiewicz and H. Stumpf, 'Theory and numerical analysis of shells undergoing large elastic strains,' Int. J. Solids Struct., 29, 689-709, 1992.
9. Y. Başar and Y. Ding, 'Finite-element analysis of hyperelastic thin shells with large strains', Comput. Mech. 18, No. 3, 200-214, 1996.
10. Y. Basar and Y. Ding, 'Shear deformation models for large-strain shell analysis.Int. J. Solids and Struct., 34, No. 14, 1687-1708, 1997.
11. R.W. Ogden, 'Non-Linear Elastic Deformations. Ellis Horwood Series in Mathematics and its Applications,' Chichester, 1984.
12. R.W. Ogden, 'Recent advances in the phenomenological theory of rubber elasticity,' Rubber Chem. Technol., 59, 361-383, 1986.
13. P. A. J. van den Bogert and R. de Borst, 'On the behaviour of rubber-like materials in compression and shear', Arch. Appl. Mech., 64, 136-146, 1994.
14. J.C. Simo and R.L. Taylor, 'Quasi-incompressible finite elasticity in principal stretches: continuum basis and numerical algorithms,' Comput. Meth. Appl. Mech. Engng., 85, 273-310, 1991.
15. A.F. Saleeb, T.Y.P. Chang and S.M. Arnold, 'On the development of explicit robust schemes for implementation of a class of hyperelastic models in large-strain analysis of rubbers,' Int. J. Numer. Meth. Engng., 33, 1237-1249, 1992.
16. -1/2 and more general isotropic tensor functions of C,' J. Elasticity, 15, 319-323, 1985.
17. K.N. Morman, 'The generalized strain measure with application to non homogeneous deformations in rubber-like solids', J. Appl. Mech. 53, 726-728, 1986.
18. G. Duffett and B.D. Reddy, 'The analysis of incompressible hyperelastic bodies by the finite element method', Comput. Meth. Appl. Mech. Engng., 41, No. 1, 105-120, 1983.
19. T. Sussman and K.-J. Bathe, 'A finite element formulation for nonlinear incompressible elastic and inelastic analysis,' Comput. Struct., 26, 1/2, 357-409, 1987.
20. S. Reese, 'Theorie und Numerik des Stabilitätsverhaltens hyperelastischer Festkörper,' Dissertationsschrift, Technische Hochschule Darmstadt, 1994.
21. P. Wriggers and R.L. Taylor, 'A fully non-linear axisymmetrical membrane element for rubber-like materials,' Engng. Comput., 7, 303-310, 1990.
22. F. Gruttmann and R.L. Taylor, 'Theory and finite element formulation of rubberlike membrane shells using principal stretches', Int. J. Numer. Meth. Engng., 35, 1111-1126, 1992.
23. R. Eberlein, P. Wriggers and R.L. Taylor, 'A fully non-linear axisymmetrical Quasi-Kirchhoff-Type shell element for rubber-like materials', Int. J. Numer. Meth. Engng., 36, 4027-4043, 1993.
24. R. Eberlein, 'Finite-Elemente-Konzepte für Schalen mit großen elastischen und plastischen Verzerrungen', Dissertation, Technische Hochschule Darmstadt, 1997.
25. K.S. Valanis and R.F. Landel, 'The strain-energy function of a hyperelastic material in terms of the extension ratios,' J. Appl. Phys., 38, 2997-3002, 1967.
26. J. Betten, 'Interpolations Methods for Tensor Functions', in: X. J. R. Avula et al. (eds.), Mathematical Modelling in Science and Technology, Rergamon Press, New York, 1984.
27. J.C. Simo and L. Vu-Quoc, 'Three dimensional finite strain rod model. Part II: Computational aspects,' Comput. Meth. Appl. Mech. Engng., 58, 79-116, 1986.
28. W. Menzel, 'Gemischt-hybride Elementformulierungen fur komplexe Schalenstrukturen unter endlichen Rotationen', Dissertationsschrift Mitteilung Nr. 96-4. Institut für konstruktiven Ingenieurbau. Ruhr-Universität Bochum, 1996.
29. E.N. Dvorkin and K.-J. Bathe, 'A continuum mechanics based four-node shell element for general nonlinear analysis', Engng. Comput., 1, 77-88, 1984.
30. Y. Başar, Y. Ding and R. Schultz, 'Refined shear-deformation models for composite laminates with finite rotations', Int. J. Solids Struct., 30, 2611-2638, 1993.
31. Y. Başar and Y. Ding, 'Interlaminar stress analysis of composites: layerwise shell finite elements including transverse strains', Composites Engng., 5, 485-499, 1995.