FE2 computational homogenization for the thermo-mechanical analysis of heterogeneous solids

Computer Methods in Applied Mechanics and Engineering

Volumn 198, Issue 3-4, 2008, Pages 602-613

  Ozdemir I ^a   Brekelmans, W A M ^a   Geers, M G D ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Coarse graining; Computational homogenization; FE2; Heterogeneous solids; Multi scale analysis; Thermo mechanics

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONSTITUTIVE EQUATIONS; DIFFERENTIAL EQUATIONS; FORMING; HOMOGENIZATION METHOD; INITIAL VALUE PROBLEMS; IRON COMPOUNDS; MATHEMATICAL OPERATORS; THERMAL SPRAYING; THERMOMECHANICAL TREATMENT;

COARSE GRAINING; COMPUTATIONAL HOMOGENIZATION; FE2; HETEROGENEOUS SOLIDS; MULTI-SCALE ANALYSIS; THERMO-MECHANICS;

THERMAL EXPANSION;

EID: 55649102280     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.09.008     Document Type: Article

References (35)

1. Hashin Z. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29 (1962) 143-150
2. Rosen B.W., and Hashin Z. Effective thermal expansion coefficients and specific heats of composite materials. Int. J. Engrg. Sci. 8 (1970) 157-173
3. Guedes J.M., and 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
4. Chung P.W., and Tamma K.K. Homogenization of temperature-dependent thermal conductivity in composite materials. AIAA J. Thermophysics Heat Transfer 15 1 (2001) 10-17
5. Chung P.W., and Tamma K.K. Woven fabric composites - developments in engineering bounds, homogenization and applications. Int. J. Numer. Methods Engrg. 45 (1999) 1757-1790
6. Golanski D., Terada K., and Kikuchi N. Macro and micro scale modeling of thermal residual stresses in metal matrix composite surface layers by the homogenization method. Comput. Mech. 19 (1997) 188-202
7. Ghosh S., and Liu Y. Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials. Int. J. Numer. Methods Engrg. 38 (1995) 1361-1398
8. Moorthy S., Ghosh S., and Liu Y.S. Voronoi cell finite element model for thermo-elastoplastic deformation in random heterogeneous media. Appl. Mech. Rev. 47 1 (2001) 207-221
9. Fish J., and Shek K.L. Finite deformation plasticity of composite structures: Computational models and adaptive strategies. Comput. Methods Appl. Mech. Engrg. 172 (1999) 145-174
10. Fish J., and Yu Q. Multiscale damage modeling for composite materials: theory and computational framework. Int. J. Numer. Methods Engrg. 52 (2001) 161-192
11. Smit R.J.M., Brekelmans W.A.M., and Meijer H.E.H. Prediction of the mechanical behaviour of non-linear heterogeneous systems by multi-level finite element modeling. Comput. Methods Appl. Mech. Engrg. 155 (1998) 181-192
12. 2 multiscale approach for modeling the elastoviscoplastic behaviour of long fibre Sic/Ti composite materials. Comput. Methods Appl. Mech. Engrg. 183 (2000) 309-330
13. Kouznetsova V.G., Brekelmans W.A.M., and Baaijens F.P.T. An approach to micro-macro modeling of heterogeneous materials. Comput. Mech. 27 (2001) 37-48
14. Miehe C., Schröder J., and Schotte J. Computational homogenization analysis in finite plasticity. Simulation of texture development in polycrystalline materials. Comput. Methods Appl. Mech. Engrg. 171 (1999) 387-418
15. Kouznetsova V.G., Geers M.G.D., and 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
16. V.G. Kouznetsova, Computational homogenization for the multi-scale analysis of multi-phase materials, Ph.D. thesis, Eindhoven University of Technology, 2002. .
17. Massart T.J., Peerlings R.H.J., and Geers M.G.D. Structural damage analysis of masonary walls using computational homogenisation. Int. J. Damage Mech. 16 (2007) 199-226
18. Geers M.G.D., Coenen E., and Kouznetsova V.G. Multi-scale computational homogenization of structured thin sheets. Model. Simulat. Mater. Sci. Engrg. 15 (2007) S393-S404
19. Matouš K., Kulkarni M.G., and Geubelle P.H. Multiscale cohesive failure modeling of heterogeneous adhesives. J. Mech. Phys. Solids 56 4 (2008) 1511-1533
20. Özdemir I., Brekelmans W.A.M., and Geers M.G.D. Computational homogenization for heat conduction in heterogeneous solids. Int. J. Numer. Methods Engrg. 73 2 (2008) 185-204
21. Nemat-Nasser S., and Hori M. Micromechanics: overall properties of heterogeneous solids. North-Holland Series in Applied Mathematics and Mechanics (1993), North-Holland
22. Kanit T., Forest S., Galliet I., Mounoury V., and Jeulin D. Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int. J. Solids Struct. 40 (2003) 3647-3679
23. Zeman J., and Šejnoha M. Numerical evaluation of effective elastic properties of graphite fiber tow impregnated by polymer matrix. J. Mech. Phys. Solids 49 1 (2001) 69-90
24. van der Sluis O., Schreurs P.J.G., Brekelmans W.A.M., and Meijer H.E.H. Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructure modelling. Mech. Mater. 32 (2000) 449-462
25. Kouznetsova V.G., Geers M.G.D., and Brekelmans W.A.M. Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy. Comput. Methods Appl. Mech. Engrg. 193 (2004) 5525-5550
26. Zhang H.W., Zhang S., Bi J.Y., and Schrefler B.A. Thermo-mechanical analysis of periodic multiphase materials by a multiscale asymptotic homogenization approach. Int. J. Numer. Methods Engrg. 69 (2007) 87-113
27. Auriault J.L. Effective macroscopic description of heat conduction in periodic composites. Int. J. Heat Mass Transfer 26 6 (1983) 861-869
28. Ostoja-Starzewski M. Towards stochastic continuum thermodynamics. J. Non-equilibrium Thermodyn. 27 (2002) 335-348
29. McMeeking R.M., and Rice J.R. Finite element formulations for large elastic-plastic deformations. Int. J. Solids Struct. 11 (1975) 601-616
30. Bonet J., and Wood R.D. Nonlinear Continuum Mechanics for Finite Element Analysis (1997), Cambridge University Press
31. Simo J.C., and Hughes J.T. Computational Inelasticity Interdisciplinary Applied Mathematics (2000), Springer-Verlag
32. Byun T.S., and Kim I.S. Stress and strain partition in elastic and plastic deformation of two phase alloys. J. Mater. Sci. 26 (1991) 3917-3925
33. Bouaziz O., and Buessler P. Iso-work increment assumption for heterogeneous material behaviour. Adv. Engrg. Mater. 6 (2004) 79-83
34. Nye J.F. Physical Properties of Crystals (1985), Oxford University Press, Oxford
35. In: Swain M. (Ed). Structure and Properties of Ceramics Materials Science and Technology vol. 11 (1994), VCH