Validation of a numerical method based on Fast Fourier Transforms for heterogeneous thermoelastic materials by comparison with analytical solutions

Computational Materials Science

Volumn 87, Issue , 2014, Pages 209-217

  Anglin, B S ^a   Lebensohn, R A ^b   Rollett, A D ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Eshelby inclusion problem; FFT based spectral method; Micromechanical fields; Thermal stresses; Thermoelasticity

Indexed keywords

FAST FOURIER TRANSFORMS; ITERATIVE METHODS; NUMERICAL METHODS; SPECTROSCOPY; THERMAL STRESS; THERMOELASTICITY;

ANALYTICAL RESULTS; ESHELBY INCLUSION PROBLEM; HETEROGENEOUS MATERIALS; INHOMOGENEOUS INCLUSIONS; MICRO-MECHANICAL; SPECTRAL METHODS; THERMOELASTIC MATERIALS; THERMOELASTIC RESPONSE;

INCLUSIONS;

EID: 84896329562     PISSN: 09270256     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.commatsci.2014.02.027     Document Type: Article

References (40)

1. A.S. Bouchikhi J. Mater. Sci. Technol. 17 2009 103 116
2. H. Chen, W. Hu, A. Atiser, Y. Zhong, and G. Gottstein Int. J. Mater. Res. 97 2006 1320 1327
3. X. Tian, Y. Shen, C. Chen, and T. He Int. J. Solids Struct. 43 2006 2050 2063
4. M. Duflot Int. J. Numer. Methods Eng. 74 2008 827 847
5. N. Mukherjee, and P. Sinha Compos. Struct. 34 1996 1 12
6. L. Aminallah, T. Achour, B.B. Bouiadjra, B. Serier, A. Amrouche, X. Feaugas, and N. Benssediq Comput. Mater. Sci. 46 2009 1023 1027
7. A. Zamani, and M.R. Eslami Int. J. Solids Struct. 47 2010 1392 1404
8. W.-H. Chen, and K. Ting Nucl. Eng. Des. 90 1985 55 65
9. Y. Guyot, C. Malhaire, M.L. Berre, B. Champagnon, A. Sibai, E. Bustarret, and D. Barbier Mater. Sci. Eng., B 46 1997 24 28
10. J. Wall, H. Choo, T.N. Tiegs, and P.K. Liaw Mater. Sci. Eng., A 421 2006 40 45
11. M.K. Apalak, and R. Gunes J. Thermoplast. Compos. Mater. 18 2005 119 152
12. N. Strömberg Comput. Methods Appl. Mech. Eng. 177 1999 441 455
13. V. Vedula, S. Glass, D. Saylor, G. Rohrer, W. Carter, and S. Langer J. Am. Ceram. Soc. 84 2001 2947 2954
14. A. Skwarek, M. Pluska, J. Ratajczak, A. Czerwinski, K. Witek, and D. Szwagierczak Mater. Sci. Eng., B 176 2011 352 357
15. M. Dittes, P. Oberndorff, P. Crema, V. Schroeder, Tin whisker formation in thermal cycling conditions, in: Proceedings 2003 Electronics Packaging Technology Conference, 2003, pp. 183-188.
16. J.W. Shin, and E. Chason J. Mater. Res. 24 2009 1522 1528
17. T. Terasaki, T. Iwasaki, Y. Okura, T. Suzuki, Evaluation of tin-whisker growth during thermal-cycle testing using stress- and mass-diffusion analysis, in: Proceedings 2009 Electronic Components and Technology Conference, 2009, pp. 277-284.
18. J.H. Zhao, P. Su, M. Ding, S. Chopin, and P.S. Ho IEEE Trans. Electron. Packag. Manuf. 29 2006 265 273
19. H. Moulinec, and P. Suquet Comput. Methods Appl. Mech. Eng. 157 1998 69 94
20. J.C. Michel, H. Moulinec, and P. Suquet Comput. Methods Appl. Mech. Eng. 172 1999 109 143
21. J.C. Michel, H. Moulinec, and P. Suquet Comput. Model. Eng. Sci. 1 2000 79 88
22. J.C. Michel, H. Moulinec, and P. Suquet Int. J. Numer. Methods Eng. 52 2001 139 160
23. F. Willot, Y.P. Pellegrini, M.I. Idiart, and P. Ponte Castaneda Phys. Rev. B 78 2008 104111
24. S. Brisard, and L. Dormieux Comput. Mater. Sci. 49 2010 663 671
25. V. Monchiet, and G. Bonnet Int. J. Numer. Methods Eng. 89 2012 1419 1436
26. V. Vinogradov, and G.W. Milton Int. J. Numer. Methods Eng. 76 2008 1678 1695
27. M.I. Idiart, F. Willot, Y.P. Pellegrini, and P. Ponte Castaneda Int. J. Solids Struct. 46 2009 3365 3382
28. R.A. Lebensohn Acta Mater. 49 2001 2723 2737
29. R.A. Lebensohn, R. Brenner, O. Castelnau, and A.D. Rollett Acta Mater. 56 2008 3914 3926
30. R. Brenner, R.A. Lebensohn, and O. Castelnau Int. J. Solids Struct. 46 2009 3018 3026
31. R.A. Lebensohn, A.K. Kanjarla, and P. Eisenlohr Int. J. Plast. 32-33 2012 59 69
32. F. Grennerat, M. Montagnat, O. Castelnau, P. Vacher, H. Moulinec, P. Suquet, and P. Duval Acta Mater. 60 2012 3655 3666
33. D.J. Eyre, and G.W. Milton J. Phys. III 6 1999 41 47
34. J. Eshelby Math. Phys. Sci. 241 1957 376 396
35. T. Mura Micromechanics of Defects in Solids 1991 Kluwer Academic Publishers Dordrecht, Netherlands
36. G. Scherer Relaxation in Glass and Composites 1986 J Wiley & Sons New York
37. R.A. Lebensohn, M.I. Idiart, and P. Ponte Philos. Mag. 91 2011 3038 3067
38. M. Frigo, and S.G. Johnson Proc. IEEE 93 2005 216 231
39. A. Vattré, B. Devincre, F. Feyel, R. Gatti, S. Groh, O. Jamond, and A. Roos J. Mech. Phys. Solids 63 2014 491 505
40. J. Li, X.X. Tian, and R. Abdelmoula Int. J. Fract. 173 2012 135 146