Consistent gradient formulation for a stable enhanced strain method for large deformations

Engineering Computations (Swansea, Wales)

Volumn 13, Issue 1, 1996, Pages 103-123

  Korelc, Jože ^a   Wriggers, Peter ^b  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; INTEGRATION; INTERPOLATION; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; STABILIZATION; STRAIN; TENSORS; VARIATIONAL TECHNIQUES; BIFURCATION (MATHEMATICS); COMPUTATIONAL METHODS; DEFORMATION; PLASTICITY; STIFFNESS MATRIX; STRESSES;

ARTIFICIAL HOUR GLASS CONTROL; BIOLA-KIRCHHOFF STRESS TENSOR; CONSISTENT GRADIENT FORMULATION; DEFORMATION TENSOR; HOUR GLASS MODE; HYBRID STRESS METHOD; HYPERELASTIC MATERIAL LAW; QUADRILATERAL ELEMENT FORMULATIONS; STABLE ENHANCED STRAIN METHOD; THREE FIELD HU-WASHIZU FUNCTIONAL; CONSISTENT GRADE FORMULATION; HOUR-GLASS MODES; HYPERELASTIC ELEMENTS; ORTHOGONALITY CONDITIONS;

DEFORMATION; STRAIN;

EID: 0029734327     PISSN: 02644401     EISSN: None     Source Type: Journal    
DOI: 10.1108/02644409610111001     Document Type: Article

References (20)

1. Simo, J.C. and Rifai, M.S., "A class of mixed assumed strain methods and the method of incompatible modes", International Journal of Numerical Methods in Engineering, No. 29, 1990, pp. 1595-638.
2. Andelfinger, U. and Ramm, E., "EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements", International Journal of Numerical Methods in Engineering, No. 36, 1993, pp. 1311-37.
3. Korelc, J. and Wriggers, P., Efficient Enhanced Strain Element Formulation for 2D and 3D problems, Advances in finite element technology, A Series of Handbooks on Theory and Engineering Applications of Computational Methods, CIMNE, Barcelona, 1995, pp. 22-46.
4. Piltner, R. and Taylor, R.L., "A quadrilateral mixed finite element with two enhanced strain modes", International Journal of Numerical Methods in Engineering, No. 38, 1995, pp. 1783-808.
5. Simo, J.C. and Armero, F., "Geometrically nonlinear enhanced mixed methods and the method of incompatible modes", International Journal of Numerical Methods in Engineering, No. 33, 1992, pp. 1413-49.
6. Simo, J.C., Armero, F. and Taylor, R.L., "Improved version of assumed enhanced strain trilinear element for 3D finite deformation problems", Computer Methods in Applied Mechanics and Engineering, No. 110, 1993, pp. 359-86.
7. de Souza Neto, E.A., Peric, D., Huang, G.C. and Owen, D.R.J., "Remarks on the stability of enhanced strain elements in finite elasticity and elastoplasticity", Computational Plasticity, Fundamentals and Applications, Proceedings of the 4th International Conference, Pineridge Press, Swansea, 1995, pp. 361-72.
8. Wriggers, P. and Reese, S., "A note on enhanced strain methods for large deformations", submitted to Computer Methods in Applied Mechanics and Engineering.
9. Crisfield, M.A., Incompatible Modes, Enhanced Strain and Substitute Strains for Continuum Elements, Advances in finite element technology, A Series of Handbooks on Theory and Engineering Applications of Computational Methods, CIMNE, Barcelona, 1995, pp. 47-61.
10. Crisfield, M.A., Moita, G.F., Jelenic, G. and Lyons, L.P.R., "Enhanced lower-order element formulations for large strains", in Computational Plasticity, Fundamentals and Applications, Proceedings of the 4th International Conference, Pineridge Press, Swansea, 1995, pp. 361-72.
11. Taylor, R.L., Beresford, P.J. and Wilson, E.L., "A non-conforming element for stress analysis", International Journal of Numerical Methods in Engineering, No. 10, 1976, pp. 1211-19.
12. Wilson, E.L., Taylor, R.L., Dohertyn, W.P. and Ghaboussi, J., Incompatible Displacement Models, Academic Press, New York, NY, 1973.
13. Korelc, J., "SMS - symbolic mechanics system", Technical report 1/95, Institut fur Mechanik, Technische Hochschule, Darmstadt, Germany, 1995.
14. Wolfram, S., Mathematica: A System for Doing Mathematics by Computer, Addison-Wesley, Reading, MA, 1991.
15. Sussman, T. and Bathe, K.-J., "A finite element formulation for nonlinear incompressible elastic and inelastic analysis", Computers & Structures, Vol. 26 Nos 1/2, 1987, pp. 357-409.
16. Reese, S. and Wriggers, P., "A finite element method for stability problems in finite elasticity", International Journal of Numerical Methods in Engineering, No. 38, 1995, pp. 1171-200.
17. Li, X., Crook, A.J.L. and Lyons, L.P.R., "Mixed strain elements for non-linear analysis", Engineering Computations, No. 10, 1993, pp. 223-42.
18. Liu, W.K., Hu, Y.-K. and Belytschko, T., "Multiple quadrature underintegrated finite elements", International Journal of Numerical Methods in Engineering, No. 37, 1994, pp. 3263-89.
19. Reddy, B.D. and Simo, J.C., "Stability and convergence of a class of enhanced strain methods", Technical report, Centre for Research in Computational and Applied Mechanics, University of Cape Town, South Africa, 1992.
20. Zhu, Y.Y. and Cescotto, S., "Unified and mixed formulation of the 4-node quadrilateral elements by assumed strain method: Application to thermomechanical problems", International Journal of Numerical Methods in Engineering, No. 38, 1995, pp. 685-716.