An extension of Herrmann's principle to nonlinear elasticity

Applied Mathematical Modelling

Volumn 21, Issue 2, 1997, Pages 97-107

  Shariff, M H B M ^a  

^a TEESSIDE UNIVERSITY   (United Kingdom)

Author keywords

Finite element; Incompressible; Nonlinear elasticity; Slightly compressible

Indexed keywords

COMPRESSIBILITY; COMPUTER SIMULATION; ELASTICITY; FINITE ELEMENT METHOD; NONLINEAR EQUATIONS; PLASTIC DEFORMATION;

DISPLACEMENT FIELDS; HERRMAN PRINCIPLE; NONLINEAR ELASTICITY; SLIGHTLY COMPRESSIBLE;

VARIATIONAL TECHNIQUES;

EID: 0031072180     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0307-904X(96)00151-5     Document Type: Article

References (37)

1. Fried, I. Influence of Poisson's ratio on the condition of the finite elements stiffness matrix. Int. J. Sol. Struct. 1973, 9, 323-329
2. Brezzi, F. and Fortin, M. Mixed and Hybrid Finite Element Methods. Springer, New York, 1991
3. Hughes, T. J. R. The Finite Element Method-Linear Static and Dynamic Finite Element Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1987
4. Fried, I. Finite clement analysis of incompressible material by residual energy balancing. Int. J. Sol. Struct. 1974, 10, 993-1002
5. Skala, D. P. Large strain finite analysis for a compressible elastomeric material. Proc. Symp. Appl. Comp. Meth. Engng., Los Angeles, 1977
6. Hughes, T. J. R., Taylor, R. L. and Sackman, J. L. Finite element formulation and solution of contact and impact problems in continuum mechanics - III. Report 75-7, Berkeley, University of California, 1975
7. Cescotto, S. and Fonder, G. A finite element approach for large strains of nearly incompressible rubber-like materials. Int. J. Sol. Struct. 19 79, 15, 589-605.
8. Shariff, M. H. B. M. Parallel finite software for nonlinear stress problems. Parallel Computing and Transputer Applications, eds. M. Valero. IOS Press, Amsterdam, 1992, pp. 1261-1270
9. Bercovier, M., Hasbani, Y., Gilon, Y. and Bathe, K. J. On a finite element procedure for non-linear in compressible elasticity. Hybrid and Mixed Finite Element Methods, eds. S. N. Alturi, R. H. Gallagher, and O. C. Zienkiewicz. Wiley-Interscience. New York, 1983
10. Shariff, M. H. B. M. Linear finite-element equations for nonlinear deformation of slightly compressible elastic material. Q. J. Much. Appl. Math. 1992, 45, 169-181
11. Meihe, C. Aspects of the formulation and finite element implementation of large strain isotropic elasticity. Int. J. Numer. Methods Eng. 1994, 37, 1981-2004
12. Jinka, A. G. K. and Lewis, R. L. Incompressibility and axisymmetry: A modified mixed and penalty formulation. Int. J. Numer. Methods Eng. 1994, 37, 1623-1649
13. Hueck, U. and Schreyer, H. L. The use of orthogonal projections to handle constraints with applications to incompressible four-node quadrilateral elements. Int. J. Numer. Methods Eng. 1992, 35, 1633-1661
14. Tsinopoulos, S. V., Polyzos, D. and Beskos, D. E. BEM formulation for (3D) elastic incompressible solids. Advances in Boundary Element Methods, ed. B. H. V. Topping. Civil-Comp Press, Edinburgh, 1996, pp. 1-8
15. Fenner, R. T. and Remzi, R. M. A. Boundary integral equation of compression moduli of bonded rubber blocks. J. Strain Anal. 1983, 18, 217-223
16. Al-Gahtani, H. J. and Altiero, N. J. Application of the boundary element method to rubber-like elasticity. Appl. Math. Modelling 1996, 20, 654-661
17. Phan-Tien, N. BEM for finite-elasticity, Comput. Mech. 1990, 6, 205-219
18. Herrmann, L. R. Elasticity equations for incompressible and nearly incompressible materials by a variational theorem. AIAAJ 1965, 3, 1896-1900
19. Babuska, I. and Suri, M. Locking effects in the finite element approximation of elasticity problems. Numer. Math. 1992, 62, 439-463
20. Ogden, R. W. Nearly isochoric deformations: Application to rubberlike solids. J. Mech Phys. Solids 1978, 26, 37-57
21. PERFINE - The Manual, Barrett eds. 1989
22. Shariff, M. H. B. M. Nonlinear elasticity equations for slightly compressible and incompressible materials by a variational theorem. Report No. TEES-SCM-1-94, University of Teesside, 1994
23. Shariff, M. H. B. M. Variational principles for compressible and incompressible anisotropic rubberlike materials. Submitted for publications
24. Blatz, P. J. Application of finite elasticity theory in predicting the performance of solid propellent motors. California Institute of Technology, GALCIT SM60-25, 1960
25. Shariff, M. H. B. M. A constrained element-by-element method for slightly compressible and incompressible materials and its parallel implementation on transputers. Advances in Parallel and Vector Processing for Structural Mechanics, eds. B. H. V. Topping, and M. Papadrakakis. Civil-Comp Press, Edinburgh, 1994, pp. 53-57
26. Niu, O. and Shepard, M. S. Superconvergent boundary stress extraction and some experiments with adaptive pointwise error control. Int. J. Numer. Methods Eng. 1994, 37, 877-891
27. Herrmann, L. R. and Toms, R. M. A reformulation of the elastic field equations in terms of displacements, valid for all admissible values of Poisson's ratio. J. Appl. Mech. 1964, 31, 148-149
28. Zienkiewicz, O. C. The Finite Element Method, 3rd Edition. McGraw-Hill, UK, 1977
29. Green, A. E. and Zerna, W. Theoretical Elasticity, 2nd Edition. Clarendon Press, Oxford, 1968
30. Oden, J. T. Finite Elements of Nonlinear Continua. McGraw-Hill, New York, 1972
31. Shariff, M. H. B. M. An analysis of non-linear deformation of bonded rubber mounts. Proc. Instn. Mech. Engrs. 1989, 203, 113-119
32. Petrie, C. J. S. and Shariff, M. H. B. M. Finite deformation of compressible bonded rubber mounts. J. Strain Analysis 1992, 27, 157-169
33. Shariff, M. H. B. M. A general approach to axial deformation of bonded elastic mounts of various cross-sectional shapes. Appl. Math. Modelling 1993, 17, 430-436
34. Ogden, R. W. Non-linear Elastic Deformation. Ellis Horwood, Chichester, 1984
35. Gent, A. N. and Lindley, P. B. Compression of bonded rubber blocks. Proc. Instn. Mech. Engrs. 1959, 173, 111-117
36. Penn, R. W. Volume changes accompanying the extension of rubber. Trans. Soc. Rheol. 1970, 14, 509-517
37. Ogden, R. W. Volume changes associated with the deformation of rubber-like solids. J. Mech. Phys. Solids 1976, 24, 323-338