Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strain

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 31-32, 2003, Pages 3531-3563

  Terada, K ^a   Saiki, I ^b   Matsui, K ^a   Yamakawa, Y ^c  

^a TOHOKU UNIVERSITY   (Japan)

^b UTSUNOMIYA UNIVERSITY   (Japan)

^c NAGAOKA UNIVERSITY OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; LINEARIZATION; MATERIALS SCIENCE; STRAIN;

TWO-SCALE KINEMATICS;

KINEMATICS;

HETEROGENEOUS MEDIUM; STRAIN;

EID: 0042125263     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00365-7     Document Type: Article

References (44)

1. Benssousan A. Lions J.-L. Papanicoulau G. Asymptotic Analysis for Periodic Structures 1978 North-Holland Amsterdam
2. Sanchez-Palencia E. Non-homogeneous media and vibration theory Lecture Notes in Physics 127 1980 Springer-Verlag Berlin
3. Lions J.-L. Some Methods in Mathematical Analysis of Systems and their Control 1981 Kexue Chubanshe Science Press and Gordon - Breach Science Pub. Beijing
4. Bakhvalov N. Panasenko G. Homogenization: Averaging Processes in Periodic Media 1984 Kluwer Academic Pub. Dordrecht
5. Devries F. Léné F. Homogenization at set macroscopic stress: numerical implementation and application Recherche Aerospatiale 1 1987 34-51
6. Guedes J.M. Kikuchi N. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods Comput. Methods Appl. Mech. Engrg. 83 1990 143-198
7. Paumelle P. Hassim A. Léné F. Microstress analysis in woven composite structures Recherche Aerospatiale 6 1991 47-62
8. Ghosh S. Lee K. Moorthy S. Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method Int. J. Solids Struct. 32 1 1995 27-62
9. Anthoine A. Derivation of the in-plane elastic characteristics of masonry through homogenization theory Int. J. Solids Struct. 32 2 1995 137-163
10. Suquet P.M. Local and global aspects in the mathematical theory of plasticity Sawczuk A. et al Plasticity Today 1985 279-309 Elsevier Applied Science Pub. London
11. Suquet P.M. Elements of homogenization theory for inelastic solid mechanics Homogenization Techniques for Composite Media Sanchez-Palencia E. Zaoui A. Lecture Note on Physics 272 1987 193-278 Springer-Verlag Berlin
12. Léné F. Leguillon D. Homogenized constitutive law for a partially cohesive composite material Int. J. Solids Struct. 18 5 1982 443-458
13. Devries F. Dumontet H. Duvaut G. Léné F. Homogenization and damage for composite structures Int. J. Numer. Methods Engrg. 27 1989 285-298
14. Jansson S. Homogenized nonlinear constitutive properties and local stress concentrations for composites with periodic internal structure Int. J. Solids Struct. 29 17 1992 2181-2200
15. Swan C.C. Cakmak A.S. A hardening orthotropic plasticity model for non-frictional composites: rate formulation and integration algorithm Int. J. Numer. Methods Engrg. 37 5 1994 839-860
16. Swan C.C. Techniques for stress- and strain-controlled homogenization of inelastic periodic composites Comput. Methods Appl. Mech. Engrg. 117 3-4 1994 249-267
17. Ghosh S. Moorthy S. Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi cell finite element method Comput. Methods Appl. Mech. Engrg. 121 1-4 1995 373-409
18. Terada K. Kikuchi N. A class of general algorithms for multi-scale analyses of heterogeneous media Comput. Methods Appl. Mech. Engrg. 190 40-41 2001 5427-5464
19. Michel J.C. Moulinec H. Suquet P. Effective properties of composite materials with periodic microstructure: a computational approach Comput. Methods Appl. Mech. Engrg. 172 1-4 1999 109-143
20. Miehe C. Schroder J. Schotte J. Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials Comput. Methods Appl. Mech. Engrg. 171 3-4 1999 387-418
21. Kouznetsova V. Geers M.G.D. Brekelmans W.A.M. Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme Int. J. Numer. Methods Engrg. 54 2002 1235-1260
22. Car E. Zalamea F. Oller S. Miquel J. Oñate E. Numerical simulation of fiber reinforced composite materials--two procedures Int. J. Solids Struct. 39 2002 1967-1986
23. Suquet P.M. Overall potentials and external surfaces of power law or ideally plastic composites J. Mech. Phys. Solids 41 6 1993 981-1002
24. Chung P.W. Tamma K.K. Woven fabric composites--developments in engineering bounds, homogenization and applications Int. J. Numer. Methods Engrg. 45 12 1999 1757-1790
25. K. Terada, N. Kikuchi, Nonlinear homogenization method for practical applications, in: S. Ghosh, M. Ostoja-Starzewski (Eds.), Computational Methods in Micromechanics, AMSE AMD 212, 1995, pp. 1-16
26. Ghosh S. Kyunghoon L. Moorthy S. Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model Comput. Methods Appl. Mech. Engng. 132 1-2 1996 63-116
27. Fish J. Shek K. Pandheeradi M. Shephard M. Computational plasticity for composite structures based on mathematical homogenization: theory and practice Comput. Methods Appl. Mech. Engrg. 148 1-2 1997 53-73
28. Pellegrino C. Galvanetto U. Schrefler B.A. Numerical homogenization of periodic composite materials with non-linear material components Int. J. Numer. Methods Engrg. 46 10 1999 1609-1637
29. Fish J. Shek K. Finite deformation plasticity for composite structures: computational models and adaptive strategies Comput. Methods Appl. Mech. Engrg. 172 1-4 1999 145-174
30. Smit R.J.M. Brekelmans W.A.M. Meijer H.E.H. Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling Comput. Methods Appl. Mech. Engrg. 155 1-2 1998 181-192
31. Gänser H.-P. Fischer F.D. Werner E.A. An iterative method for coupling of deformation and failure mechanisms on different length scales Int. J. Numer. Methods Engrg. 48 4 2000 595-611
32. Allaire G. Homogenization and two-scale convergence SIAM J. Math. Anal. 23 1992 1482-1518
33. Allaire G. Mathematical approaches and methods Hornung U. Homogenization and Porous Media 1996 225-250 Springer-Verlag New York
34. Washizu K. Variational Methods in Elasticity and Plasticity third ed. 1982 Pergamon Press New York
35. Simo J.C. Numerical analysis and simulations of plasticity Ciarlet P.G. Lions J.-L. Handbook of Numerical Analysis vol. VI 1995 183-502 North-Holland Amsterdam
36. Simo J.C. Hughes T.J.R. Computational Inelasticity 1998 Springer-Verlag New York
37. Ciarlet P.G. Mathematical Elasticity. I. Three-Dimensional Elasticity 1988 North-Holland Amsterdam
38. Tartar L. Nonlinear constitutive relations and homogenization De La Penha G.M. Medeiros L.A.J. Contemporary Developments in Continuum Mechanics and Partial Differential Equations 1978 472-484 North-Holland Amsterdam
39. K. Matsui, K. Terada, K. Yuge, Toward practical applications of two-scale analysis method for periodic heterogeneous solids in the framework of small strain elastoplasticity, Preprint
40. Hughes T.J.R. Pister K.S. Consistent linearisation in mechanics of solids and structures Comput. Struct. 8 1978 391-397
41. Marsden J.E. Hughes T.J.R. Mathematical Foundations of Elasticity 1983 Prentice-Hall Englewood Cliffs, NJ
42. Müller S. Homogenization of nonconvex integral functionals and cellular elastic materials Arch. Rat. Mech. Anal. 99 1987 189-212
43. Geymonat G. Müller S. Triantafyllidis N. Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity Arch. Rat. Mech. Anal. 122 1993 231-290
44. Saiki I. Terada K. Ikeda K. Hori M. Appropriate number of unit cells in a representative volume element for microstructural bifurcation encountered in a multi-scale modeling Comput. Methods Appl. Mech. Engrg. 191 2002 2561-2585