On enhanced strain methods for small and finite deformations of solids

Computational Mechanics

Volumn 18, Issue 6, 1996, Pages 413-428

  Wriggers, P ^a   Korelc, J ^a,b  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIBILITY; COMPUTER SIMULATION; DEFORMATION; SOLIDS;

INCOMPRESSIBILITY;

MECHANICS;

EID: 0030261790     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00350250     Document Type: Article

References (63)

1. Andelfinger, U.; Ramm, E. 1993: EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements. Int. J. Numerical Methods in Engineering, 36: 1311-1337
2. Andelfinger, U.; Ramm, E.; Roehl, D. 1992: 2D-and 3D-enhanced assumed strain elements and their application in plasticity. In D.R.J. Owen, E. Onate, and E. Hinton, editors, Computational Plasticity, Proceedings of the 4th International Conference, pages 1997-2007. Pineridge Press, Swansea, U. K.
3. Atluri, S. N. 1973: On the hybrid stress finite element model in incremental analysis of large deflection problems. Int. J. Solids and Structures, 9: 1188-1191
4. Atluri, S. N. 1975: On hybrid finite-element models in solid mechanics. In R. Vishnevetsky, editor, Advances in Computer Methods for Partial Differential Equations, pages 346-356, AICA, Rutgers University, New Brunswick, New Jersey
5. Atluri, S. N. 1980: On some new general and complementary energy theorems for the rate problems in finite strain, classical elastoplasticity. J. Struct. Mech., 8(1): 61-92
6. Atluri, S. N.; Cazzani, A. 1995: Rotations in computational solid mechanics. Archives of Computational Methods in Engineering, 2 (1): 49-138
7. Atluri, S. N.; Murakawa, H. 1977: On hybrid finite element models in nonlinear solid mechanics. In P. Bergan, editor, Finite Elements in Nonlinear Mechanics, pages 3-40. Tapir, Trondheim
8. Atluri, S. N.; Reissner, E. 1989: On the formulation of variational theorems involving volume constraints. Computational Mechanics, 5: 337-344
9. Belytschko, T.; Ong, J. S.-J.; Liu, W. K.; Kennedy, J. M. 1984: Hourglass control in linear and nonlinear problems. Computer Methods in Applied Mechanics and Engineering, 43: 251-276
10. Crisfield, M. A. 1995: Incompatible modes, enhanced strain and substitute strains for continuum elements. In N.-E. Wiberg, editor, Advances in finite element technology, A Series of Handbooks on Theory and Engineering Applications of Computational Methods, pages 47-61. CIMNE, Barcelona
11. Crisfield, M. A.; Motia, G. F.; Jelenic, G.; Lyons, L. P. R. 1995: Enhanced lower-order element formulations for large strains. In Computational Plasticity, Fundamentals and Applications, Proceedings of the 4th International Conference, pages 293-320. Pineridge Press, Swansea, U.K.
12. Felippa, C. A.; Haugen, B. 1995: From the individual element test to finite element templates: Evolution of the patch test. Int. J. Numerical Methods in Engineering, 38: 199-229
13. Flanagan, D. P.; Belytschko, T. 1981: A uniform strain hexahedron and quadrilateral with orthogonal hourglass control Int. J. Numerical Methods in Engineering, 17; 679-706
14. Freischlager, C.; Schweizerhof, K. 1995: On a systematic development of trilinear 3D solid elements based on Simo's enhanced strain formulation. submitted to Computers & Structures
15. de Veubeke, B. F. 1965: Displacement and equilibrium models in the finite element method. In O. C. Zienkiewicz and G. C. Holister, editors, Stress Analysis. Wiley, London
16. Gruttmann, F.; Wanger, W.; Wriggers, P. 1992: A nonlinear quadrilateral shell element with drilling degrees of freedom. Ing. Archiv, 62: 474-486
17. Hughes, T. R. J. 1980: Generalization of selective integration procedures to anisotropic and nonlinear media. Int. J. Numerical Methods in Engineering, 15: 1413-1418
18. Hughes, T. R. J. 1987: The Finite Element Method: Linear Static and Dynamic Finite Elemenet Analysis. Prentice-Hall, Englewood Cliffs, New Jersey
19. Hughes, T. R. J.; Brezzi, F. 1989: On drilling degrees of freedom. Computer Methods in Applied Mechanics and Engineering, 72: 105-121
20. Hueck, U.; Reddy, B. D.; Wriggers, P. 1993: On the stabilization of the rectangular four-node quadrilateral element. Technical report, Centre for Research in Computational and Applied Mechanics, University of Cape Town, South Africa, 1993
21. Hueck, U.; Wriggers, P. 1995: A formulation for the 4-node quadrilateral element. Int. J. Numerical Methods in Engineering, 38: 3007-3037
22. Ibrahimbegovic, A.; Taylor, R. L.; Wilson, E. L. 1990: A robust quadrilateral membrane element with drilling degrees of freedom. Int. J. Numerical Methods in Engineering, 30: 445-457
23. Iura, M.; Atluri, S. N. 1992: Formulation of a membrane finite element with drilling degrees of freedom. Computational Mechanics, 9:417-428
24. Korelc, J. 1995: SMS-Symbolic Mechanics System. Technical Report 1/95, Institut for Mechanics, Technical University of Darmstadt, Germany
25. Korelc, J.; Wriggers, P. 1995: Efficient enhanced strain element formulation for 2D and 3D problems. In N.-E. Wiberg, editor, Advances in Finite Element Technology, A Series of Handbooks on Theory and Engineering Applications of Computational Methods, pages 22-46. CIMNE, Barcelona
26. Korelc, J.; Wriggers, P. 1996a: Consistent gradient formulation for a stable enhanced strain method for large deformations. Engineering Computations, 13(1): 103-123
27. Korelc, J.; Wriggers, P. 1996b: An efficient 3D enhanced strain element with Taylor expansion of the shape functions. To appear in Computational Mechanics
28. Korelc, J.; Wriggers, P. 1996c: Improved enahnced strain four node element with Taylor expansion of the shape functions. To appear in Int. J. Numerical Methods in Engineering
29. Liu, W. K.; Belytschko, T.; Chen, J.-S. 1988: Nonlinear version of flexurally superconvergent elements. Computer Methods in Applied Mechanics and Engineering, 71: 241-258
30. Li, X.; Crook, A. J. L.; Lyons, L. P. R. 1993: Mixed strain elements for non-linear analysis. Engineering Computations, 10: 223-242
31. Liu, W. K.; Hu, Y.-K.; Belytschko, T. 1994: Multiple quadrature under-integrated finite elements. Int. J. Numerical Methods in Engineering, 37: 3263-3289
32. Liu, W. K.; Ong, J. S. J.; Uras, R. A. 1985: Finite element stabilization matrices - a unified approach. Computer Methods in Applied Mechanics and Engineering, 53: 13-46
33. Marsden, J. E.; Hughes, T. R. J. 1983: Mathematical Foundation of Elasticity. Prentice-Hall, Englewood Cliffs, New Jersey
34. Miche, C. 1994: Aspects of the formulation and finite element implementation of large strain isotropic elasticity. Int. J. Numerical Methods in Engineering, 37: 1981-2004
35. Moita, G. F. 1994: Non-linear Finite Element Analysis of Continua with Emphasis on Hyperelasticity. Ph. D. Thesis, Imperial College, London.
36. Neto, E. A. S.; Peric, D.; Huang, G. C.; Owen, D. R. J. (1995): Remarks on the stability of enhanced strain elements in finite elasticity and elastoplasticity. In Computational Plasticity, Fundamentals and Applications, Proceedings of the 4th International Conference, pages 361-372. Pineridge Press, Swansea, U. K.
37. Ogden, R. W.: Non-linear Elastic Deformations. Ellis Horwood Limited, Chichester, U. K.
38. Pian, T. H. H. 1964: Derivation of element stiffness matrices by assumed stress distribution. AIAA Journal, 2: 1333-1336
39. Pian, T. H. H.; Sumihara, K. 1984: Rational approach for assumed stress finite elements. Int. J. Numerical Methods in Engineering, 20: 1685-1695
40. Pian, T. H. H.; Tong, P. 1986: Relations between incompatible displacement model and hybrid stress model. Int. J. Numerical Methods in Engineering, 22: 173-181
41. Piltner, R.; Taylor, R. L. 1995: A quadrilateral mixed finite element with two enhanced strain modes. Int. J. Numerical Methods in Engineering, 38: 1783-1808
42. Punch, E. F.; Atluri, S. N. 1984: Development and testing of stable invariant isoparametric curvilinear 2 and 3-d hybrid-stress elements. Computer Methods in Applied Mechanics and Engineering, 47: 331-356
43. Reddy, B. D.; Simo, J. C. 1995: Stability and convergence of a class of enhanced strain methods. SIAM J. Numer. Anal., 32 (6): 1705-1728, 1995
44. Reese, S.; Wriggers, P. 1995: A finite element method for stability problems in finite elasticity. Int. J. Numerical Methods in Engineering, 38: 1171-1200
45. Rubinstein, R.; Punch, E. F.; Atluri, S. N. 1983: An analysis of, and remedies for, kinematic modes in hybrid-stress finite elements: Selection of stable, invariant stress fields. Computer Methods in Applied Mechanics and Engineering, 38: 63-92
46. Seki, W.; Atluri, S. N. 1994: "Analysis of Strain Localization in Strain-Softening layperelastic meterials, using assumed stress hybrid elements" Computational Mechanics, 14, pp 549-585
47. Seki, W.; Atluri, S. N. 1995: On newly developed assumed stress finite element formulations for geometrically and materially nonlinear problems. Finite Elements in Analysis and Design, 21: 75-110
48. Simo, J. C.; Armero, F.; Taylor, R. L. 1993: Improved version of assumed enhanced strain tri-linear element for 3D finite deformation problems. Computer Methods in Applied Mechanics and Engineering, 110: 359-386
49. Simo, J. C.; Rifai, M. S. 1990: A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numerical Methods in Engineering, 29: 1595-1638
50. Simo, J. C.; Armero, F. 1992: Geometrically nonlinear enhanced mixed methods and the method of nicompatible modes. Int. J. Numerical Methods in Engineering, 33: 1413-1449
51. Simo, J. C.; Fox, D. D.; Rifai, M. S. 1989: On a stress resultant geometrically exact shell model. part II: The linear theory; computational aspects. Computer Methods in Applied Mechanics and Engineering, 73: 53-92
52. Simo, J. C.; Hughes, T. J. R. 1986: On the variational foundations of assumed strain methods. Journal of Applied Mechanics, 53: 51-54
53. Simo, J. C.; Taylor, R. L.; Pister, K. S. 1985: Variational and projection methods for the volume constraint in finite deformation plasticity. Computer Methods in Applied Mechanics and Engineering, 51: 177-208
54. Sussman, T.; Bathe, K.-J. 1987: A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Computer and Structures, 26 (1/2): 357-409
55. Sze, K. Y. 1992: Efficient formulation of robust hybrid elements using orthogonal stress/strain interpolations and admissible matrix formulation. Int. J. Numerical Methods in Engineering, 35: 1-20
56. Sze, K. Y. 1994: Finite element formulation by parametrized hybrid variational principle: Variable stiffness and removal of locking. Int. J. Numerical Methods in Engineering, 37: 2797-2818
57. Taylor, R. L.; Beresford, P. J.; Wilson, E. L. 1976: A non-comforming element for stress analysis. Int. J. Numerical Methods in Engineering, 10: 1211-1219
58. Wilson, E. L.; Taylor, R. L.; Doherty, W. P.; Ghaboussi, J. 1973: Incompatible Displacement Models, pages 43-75. Numerical and Computer Models in Structural Mechanics. Academic Press, New York
59. Wriggers, P. 1993: Continuum Mechanics, Nonlinear finite Element Techniques and Computational Stability, pages 245-287. Progress in Computational Analysis of Inelastic Structures. Springer, Wien
60. Wriggers, P.; Reese, S. 1996a: A note on enhanced strain methods for large deformations. To appear in Computer Methods in Applied Mechanics and Engineering
61. Wriggers, P.; Reese, S. 1996b: On deficiencies of enhanced strain methods in large elastic compression states. To appear in Computational Mechanics
62. Zhu, Y. Y.; Cescotto, S. 1995: Unified and mixed formulation of the 4-node quadrilateral elements by assumed strain method: Application to thermomechanical problems. Int. J. Numerical Methods in Engineering, 38: 685-716
63. Zienkiewicz, O. C.; Taylor, R. L. 1989: The Finite Element Method, Vol. 1, 4th edn. McGraw-Hill, London