Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 7, 2007, Pages 1216-1243

  Oskay, Caglar ^a   Fish, Jacob ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Composite failure; Homogenization; Multiscale method; Transformation field analysis

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; NUMERICAL ANALYSIS; NUMERICAL METHODS;

COMPOSITE FAILURE; HOMOGENIZATION; MULTIPLE SCALE ASYMPTOTIC EXPANSION METHOD; MULTISCALE METHOD; TRANSFORMATION FIELD ANALYSIS;

FAILURE ANALYSIS;

EIGENVALUES AND EIGENFUNCTIONS; FAILURE ANALYSIS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; NUMERICAL ANALYSIS; NUMERICAL METHODS;

EID: 33750965936     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.08.015     Document Type: Article

References (51)

1. Eshelby J.D. The determination of the field of an ellipsoidal inclusion and related problems. Proc. R. Soc. Lond. A 241 (1957) 376-396
2. Hashin Z. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29 (1962) 143-150
3. Mori T., and Tanaka K. Average stress in the matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21 (1973) 571-574
4. Hill R. A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13 (1965) 357-372
5. Christensen R.M., and Lo K.H. Solution for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27 (1979) 315-330
6. Babuska I. Homogenization and application: mathematical and computational problems. In: Hubbard B. (Ed). Numerical Solution of Partial Differential Equations - III, SYNSPADE (1975), Academic Press, New York
7. Benssousan A., Lions J.L., and Papanicolaou G. Asymptotic Analysis for Periodic Structures (1978), North-Holland, Amsterdam
8. Suquet P.M. Elements of homogenization for inelastic solid mechanics. In: Sanchez-Palencia E., and Zaoui A. (Eds). Homogenization Techniques for Composite Media (1987), Springer-Verlag, New York
9. Sanchez-Palencia E. Non-Homogeneous Media and Vibration Theory. Lecture Notes in Physics vol. 127 (1980), Springer-Verlag, Berlin
10. 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
11. Terada K., and Kikuchi N. Nonlinear homogenization method for practical applications. In: Ghosh S., and Ostoja-Starzewski M. (Eds). Computational Methods in Micromechanics vol. AMD-212/MD-62 (1995), ASME, New York 1-16
12. Jardak M., and Ghanem R. Spectral stochastic homogenization of divergence-type PDES. Comput. Methods Appl. Mech. Engrg. 193 6-8 (2004) 429-447
13. Ghosh S., Lee K., and Raghavan P. A multi-level computational model for multi-scale damage analysis in composite and porous materials. Int. J. Solids Struct. 38 (2001) 2335-2385
14. Zohdi T.I., Oden J.T., and Rodin G.J. Hierarchical modeling of heterogeneous bodies. Comput. Methods Appl. Mech. Engrg. 138 (1996) 273-298
15. Geers M.G.D., Kouznetsova V., and Brekelmans W.A.M. Gradient-enhanced computational homogenization for the micro-macroscale transition. J. Phys. IV 11 (2001) 145-152
16. 2 multiscale approach for modelling the elastoviscoplastic behavior of long fiber SiC/Ti composite materials. Comput. Methods Appl. Mech. Engrg. 183 (2000) 309-330
17. Giladi E., and Keller H.B. Space-time domain decomposition for parabolic problems. Numer. Math. 93 2 (2002) 279-313
18. Waisman H., and Fish J. Space-time multilevel method for molecular dynamics simulations. Comp. Methods Appl. Mech. Engrg. 195 (2006) 6542-6559
19. M. Gosz, B. Moran, J.D. Achenbach, Matrix cracking in transversely loaded fiber composites with compliant interphases, in: AMD-150/AD-32 (Ed.), Damage Mechanics in Composites, ASME, New York, 1992.
20. 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 1-4 (1995) 373-409
21. Aboudi J. A continuum theory for fiber-reinforced elastic-viscoplastic composites. J. Engrg. Sci. 20 55 (1982) 605-621
22. Dvorak G.J. Transformation field analysis of inelastic composite materials. Proc. R. Soc. Lond. A 437 (1992) 311-327
23. Bahei-El-Din Y.A., Rajendran A.M., and Zikry M.A. A micromechanical model for damage progression in woven composite systems. Int. J. Solids Struct. 41 (2004) 2307-2330
24. Moulinec H., and Suquet P. A fast numerical method for computing the linear and nonlinear properties of composites. C.R. Acad. Sci. Paris II 318 (1994) 1417-1423
25. Moulinec H., and Suquet P. A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput. Methods Appl. Mech. Engrg. 157 (1998) 69-94
26. Berlyand L.V., and Kolpakov A.G. Network approximation in the limit of small interparticle distance of the effective properties of a high-contrast random dispersed composite. Arch. Rational Mech. Anal. 159 (2001) 179-227
27. Fish J., Shek K.L., Shephard M.S., and Pandheeradi M. Computational plasticity for composite structures based on mathematical homogenization: theory and practice. Comput. Methods Appl. Mech. Engrg. 148 (1997) 53-73
28. Fish J., Yu Q., and Shek K.L. Computational damage mechanics for composite materials based on mathematical homogenization. Int. J. Numer. Methods Engrg. 45 (1999) 1657-1679
29. 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
30. Chaboche J.L., Kruch S., Maire J.F., and Pottier T. Towards a micromechanics based inelastic and damage modeling of composites. Int. J. Plasticity 17 (2001) 411-439
31. Michel J.C., and Suquet P. Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis. Comput. Methods Appl. Mech. Engrg. 193 (2004) 5477-5502
32. Dvorak G.J., and Benveniste Y. On transformation strains and uniform fields in multiphase elastic media. Proc. R. Soc. Lond. A 437 (1992) 291-310
33. Laws N. On the thermostatics of composite materials. J. Mech. Phys. Solids 21 (1973) 9-17
34. Willis J. Variational and related methods for the overall properties of composites. In: Yih C.S. (Ed). Advances in Applied Mechanics vol. 21 (1981), Academic Press, New York 1-78
35. Dvorak G.J. On uniform fields in heterogeneous media. Proc. R. Soc. Lond. A 431 (1990) 89-110
36. Raous M., Cangemi L., and Cocu M. A consistent model coupling adhesion, friction, and unilateral contact. Comput. Methods Appl. Mech. Engrg. 177 (1999) 383-399
37. Krajcinovic D. Damage Mechanics. North Holland Series in Applied Mathematics and Mechanics vol. 41 (1996), Elsevier, Amsterdam
38. Fish J., and Wagiman A. Multiscale finite element method for a locally nonperiodic heterogeneous medium. Comp. Mech. 12 (1993) 164-180
39. Levin V. Determination of the thermoelastic constants of composite materials. Mekh. Tverdogo Tels, Trans. Soviet Acad. Sciences (Mech. of Solids) 6 (1976) 137-145
40. Willis J. Variational principles and bounds for the overall properties of composites. In: Provan J.W. (Ed). Continuum Models of Discrete Systems (1978), University Waterloo Press 185-215
41. Bazant Z.P. Instability, ductility, and size effect in strain-softening concrete. J. Engrg. Mech. Div. 102 (1976) 331-344
42. Simo J.C. Strain softening and dissipation: a unification of approaches. In: Mazars J., and Bazant Z.P. (Eds). Cracking and Damage: Strain Localization and Size Effect (1989), Elsevier, New York 440-461
43. Pijaudier-Cabot G., and Bazant Z.P. Nonlocal damage theory. J. Engrg. Mech. 113 (1987) 1512-1533
44. Fish J., and Yu Q. Multiscale damage modelling for composite materials: theory and computational framework. Int. J. Numer. Methods Engrg. 52 (2001) 161-191
45. Simo J.C., and Ju J.W. Strain- and stress-based continuum damage models - I: formulation. Int. J. Solids Struct. 23 7 (1987) 821-840
46. Oden J.T., and Pires E.B. Nonlocal and nonlinear friction laws and variational principals for contact problems in elasticity. J. Appl. Mech. 50 (1983) 67-76
47. Belytschko T., Liu W.K., and Moran B. Nonlinear Finite Elements for Continua and Structures (2003), John Wiley and Sons, New York
48. Simo J.C., and Hughes T.J.R. Computational Inelasticity (1998), Springer, New York
49. Hughes T.J.R., and Winget J. Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int. J. Numer. Methods Engrg. 15 (1980) 1862-1867
50. J.M. Starbuck, R.G. Boeman, N. Rastogi, C.D. Warren, J.A. Carpenter, P.S. Sklad, Crash analysis of adhesively bonded structures, in: E.J. Wall, R. Sullivan, J.A. Carpenter (Eds.), FY 2004 Progress Report for Automotive Lightweighting Materials, US Department of Energy, 2004, pp. 221-227.
51. Oden J.T., and Vemaganti K.S. Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials - I: error estimates and adaptive algorithms. J. Comput. Phys. 164 1 (2000) 22-47