A stabilized formulation for incompressible plasticity using linear triangles and tetrahedra

International Journal of Plasticity

Volumn 20, Issue 8-9, 2004, Pages 1487-1504

  Chiumenti, M ^a   Valverde, Q ^b   Agelet de Saracibar, C ^a   Cervera, M ^a  

^a INTERNATIONAL CENTER FOR NUMERICAL METHODS IN ENGINEERING CIMNE   (Spain)

^b PONTIFICIA UNIVERSIDAD CATÓLICA DEL PERÚ   (Peru)

Author keywords

Incompressibility; Orthogonal sub grid scales; Plasticity; Stabilized finite element method

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; GALERKIN METHODS; INTERPOLATION; STRESS ANALYSIS;

INCOMPRESSIBILITY; ORTHOGONAL SUB-GRID SCALES; SOLID MECHANICS; STABILIZED FINITE ELEMENT METHOD;

ELASTOPLASTICITY;

EID: 2142641638     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2003.11.009     Document Type: Article

References (18)

1. Agelet de Saracibar C., Cervera M., Chiumenti M. On the constitutive modelling of coupled thermo-mechanical phase-change problems. Int. J. Plasticity. 17:2001;1565-1622.
2. Brezzi F., Fortin M. Mixed and Hybrid Finite Element Methods. 1991;Spinger, New York.
3. Cervera, M., Agelet de Saracibar, C., Chiumenti. M., 2002. COMET: Coupled Mechanical and Thermal Analysis. Data Input Manual. Version 5.0. Technical Report IT-308. Available: htpp://www.cimne.upc.es.
4. Chiumenti M., Valverle Q., Agelet de Saracibar C., Cervera M. A stabilized formulation for elasticity using linear displacement and pressure interpolations. Comp. Meth. in Appl. Mech. and Eng. 191:2002;3253-5264.
5. Codina R. Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods. Comp. Meth. in Appl. Mech. and Eng. 190:2000;1379-1599.
6. Garikipati K., Hughes T.J.R. A study of strain raw localization in a multiple scale framework - the one dimensional problem. Comp. Meth. in Appl. Mech. and Eng. 139:1998;193-222.
7. Garikipati K., Hughes T.J.R. A variational multiscale approach to strain localization - formulation for multidimensional problem. Comp. Meth. in Appl. Mech. and Eng. 188:2000;39-60.
8. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. 1987;Prentice-Hall, Englewood Cliffs, New Jersey.
9. Hughes T.J.R. Multiscale phenomena. Green's function, Dirichlet-to Neumann formulation, subgrid scale models, bubbles and the origins of stabilized formulations Comp. Meth. in Appl. Mech. and Eng. 127:1995;387-401.
10. Klass O., Maniatty A., Shephard M.S. A stabilized mixed finite element method for finite elasticity. Formulation for linear displacement and pressure interpolation. Comp. Meth. in Appl. Mech. and Eng. 180:1999;65-79.
11. Klass, O., Maniatty, A., Shephard, M.S., 1999b. Three dimensional stabilized finite element model for finite deformation process: In: Proceedings 7th International Symposium on Plasticity and its Current applications. Cancun. Mexico.
12. Miehe C. Aspects of the formulation and finite element implementation of large strain isotropic elasticity. Int. J. Numer. Methods in Eng. 37:1994;1981-2004.
13. Oñate, F., Rojek, J., Taylor, R.L., Zienkiewicz, O.C. Finite calculus formulation for incompressible solids using linear triangles and tetrahedra. Int. J. Numer. Methods in Eng. (submitted for publication).
14. Simo J.C., Rifai M.S. A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Methods in Eng. 29:1990;1595-1638.
15. Simo J.C., Taylor R.L., Pister K.S. Variational and projection methods for the volume constraint in finite deformation elastoplasticity. Comp. Meth. in Appl. Mech. and Eng. 51:1985;177-208.
16. Taylor, R.L., 1999. A mixed formulation for triangular and tetrahedral finite elements. In: Conference Proceedings, Metodos Numericos en la Ingenieria, SEMNI, Barcelona, Spain.
17. Zienkiewicz, O.C., Taylor, R.L., 1991. Finite Element Method, vol. 1. Fourth ed. McGraw-Hill.
18. Zienkiewicz O.C., Rojek J., Taylor R.L., Pastor M. Triangles and tetrahedra in explicit dynamic codes for solids. Int. J. Numer. Methods in Eng. 43:1998;563-583.