Complementary energy based FE modelling of coupled elasto-plastic and damage behavior for continuum microstructure computations

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 37-40, 2006, Pages 5077-5093

  Markovic, Damijan ^a,b   Ibrahimbegovic, Adnan ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b University of Colorado at Boulder   (United States)

Author keywords

Continuume microstructure computations; Damage behavior; Electro plastic behavior

Indexed keywords

ELASTICITY; ELASTOPLASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PLASTICITY; STRESSES;

CONTINUUM MICROSTRUCTURE COMPUTATIONS; DAMAGE BEHAVIOR; HETEROGENEOUS MATERIAL;

CONTINUUM MECHANICS;

CONTINUUM MECHANICS; ELASTICITY; ELASTOPLASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PLASTICITY; STRESSES;

EID: 33746929528     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.05.058     Document Type: Article

References (27)

1. J.H. Argyris, D.W. Sharpf, Methods of elasto-plastic analysis, ISD Report No. 105, University of Stuttgart, 1971.
2. Belytschko T., Moes N., Usui S., and Parimi C. Arbitrary discontinuities in finite elements. Int. J. Numer. Methods Engrg. 50 (2001) 993-1013
3. M. Bornert, T. Bretheau, P. Gilormini, Homogénéisation en mécanique des matériaux, vols. I&II, Hermes-Science, Paris.
4. Brockenbrough J.R., Suresh S., and Wienecke H.A. Deformation of metal-matrix composites with continuous fibers: geometrical effects of fiber distribution and shape. Acta Metall. Mater. 39 5 (1991) 735-752
5. Buryachenko V.A., Rammerstorfer F.G., and Plankensteiner A.F. A local theory of elastoplastic deformation of two-phase metal matrix random structure composites. J. Appl. Mech. 69 (2002) 489-496
6. Chaboche J.L., Kruch S., Maire J.F., and Potter T. Towards a micromechanics based inelastic and damage modeling of composites. Int. J. Plast. 17 (2001) 411-439
7. Dvorak G. Transformation field analysis of inelastic composite materials. Proc. Roy. Soc. London A 437 (1992) 311-327
8. Ghosh S., and Moorthy S. Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi cell finite element method. Comput. Methods Appl. Mech. Engrg. 121 (1995) 373-409
9. Gilormini P. A shortcoming of the classical non-linear extension of the self-consistent model. CR Acad. Sci. Paris 320 116 (1995) 115-122
10. Hansbo A., and Hansbo P. An unfitted finite element method, based on Nietsche's method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg. 191 47-48 (2002)
11. Hill R. Mathematical Theory of Plasticity (1950), Oxford University Press
12. Hughes T.J.R. The Finite Element Method (2000), Dover publications, Inc., Minneola, New York
13. Ibrahimbegovic A., Gharzeddine F., and Chorfi L. Classical plasticity and viscoplasticity models reformulated: theoretical and numerical implementation. Int. J. Numer. Methods Engrg. 42 (1999) 1499-1535
14. Ibrahimbegovic A., and Markovic D. Strong coupling methods in multiphase and multiscale modeling of inelastic behavior of heterogeneous structures. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3089-3107
15. Ibrahimbegovic A., Markovic D., and Gatuingt F. Constitutive model of coupled damage-plasticity and its finite element implementation. Eur. J. Finite Elem. 12 4 (2003) 381-405
16. Lemaître J., and Chaboche J.L. Mécanique des Matériaux Solides (1988), Dunod, Paris
17. Lubliner J. Plasticity Theory (1990), MacMillan, New York
18. D. Markovic, Multi-scale modeling of heterogeneous structures with nonlinear inelastic behaviors, Ph.D. thesis (in French), ENS Cachan, 2004.
19. Markovic D., and Ibrahimbegovic A. On micro-macro interface conditions for micro-scale based FEM for inelastic behavior of heterogeneous materials. Comput. Methods Appl. Mech. Engrg. 193 (2004) 5503-5523
20. Michel J.C., and Suquet P. Nonuniform transformation field analysis. Int. J. Solids Struct. 40 (2003) (special issue)
21. Needleman A., and Tvergaard V. An analysis of ductile rupture in notched bar. J. Mech. Phys. Solids 32 (1984) 461-469
22. Pian T.H.H., and Sumihara K. Rational approach for assumed stress finite elements. Int. J. Numer. Methods Engrg. 20 (1984) 1638-1685
23. Simo J.C., Kennedy J.G., and Taylor R.L. Complementary mixed finite element formulations for elastoplasticity. Comput. Methods Appl. Mech. Engrg. 74 (1989) 206-277
24. Strang G. Introduction to Applied Mathematics (1986), Addison-Wesley
25. Wilson E.L., and Ibrahimbegovic A. Use of incompatible displacement modes for the calculation of element stiffnesses or stresses. Finite Elem. Anal. Des. 7 (1990) 229-241
26. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method vols. I, II & III (2000), Butterworth Heinemann, Oxford
27. Zohdi T.I., Kachanov M., and Sevostianov I. On perfectly plastic flow in porous material. Int. J. Plast. 18 12 (2002) 1649-1659