A spectral iterative method for the computation of effective properties of elastically inhomogeneous polycrystals

Communications in Computational Physics

Volumn 11, Issue 3, 2012, Pages 726-738

  Bhattacharyya, Saswata ^a   Heo, Tae Wook ^a   Chang, Kunok ^a   Chen, Long Qing ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Elasticity; Iterative method; Spectral method

Indexed keywords

EID: 84855166604     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.290610.060411a     Document Type: Article

References (18)

1. M. Doi, Elasticity effects on the microstructure of alloys containing coherent precipitates, Prog. Mater. Sci., 40 (1996), 79.
2. P. Fratzl, O. Penrose and J. Lebowitz, Modeling of phase separation in alloys with coherent elastic misfit, J. Stat. Phys., 95 (1999), 1429.
3. L.-Q. Chen, Phase-field models for microstructural evolution, Ann. Rev. Mater. Res., 32 (2002), 113.
4. P. H. Leo, J. S. Lowengrub and H. J. Jou, A diffuse interface model for microstructural evolution in elastically stressed solids, Acta Mater., 46 (1998), 2113.
5. J. Zhu, L.-Q. Chen and J. Shen, Morphological evolution during phase separation and coarsening with strong inhomogeneous elasticity, Modell. Simul. Mater. Sci. Eng., 9 (2001), 499.
6. S. Y. Hu and L.-Q. Chen, A phase-field model for evolving microstructures with strong elastic inhomogeneity, Acta Mater., 49 (2001), 1879.
7. P. Yu, S. Y. Hu, L.-Q. Chen and Q. Du, An iterative-perturbation scheme for treating inhomogeneous elasticity in phase-field models, J. Comput. Phys., 208 (2005), 34.
8. Y. U. Wang, Y. M. Jin and A. G. Khachaturyan, Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid, J. Appl. Phys., 92 (2002), 1351. (Pubitemid 34924357)
9. Y. M. Jin, Y. U. Wang and A. G. Khachaturyan, Three-dimensional phase field microelasticity theory and modeling of multiple cracks and voids, Appl. Phys. Lett., 79 (2001), 3071.
10. D. Fan and L.-Q. Chen, Computer simulation of grain growth using a continuum field model, Acta Mater., 45 (1997), 611.
11. D. Fan, C. Geng and L.-Q. Chen, Computer simulation of topological evolution in 2-D grain growth using a continuum diffuse-interface field model, Acta Mater., 45 (1997), 1115.
12. A. G. Khachaturyan, Theory of Structural Phase Transformations in Solids, John Wiley and Sons, New York, 1983.
13. D. Y. Li and L.-Q. Chen, Shape evolution and splitting of coherent particles under applied stresses, Acta Mater., 47 (1998), 247.
14. T. Mura, Micromechanics of Defects in Solids, Springer, 1987.
15. S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Springer, 2002.
16. J. M. J. den Toonder, J. A. W. van Dommelen and F. P. T. Baaijens, The relation between single crystal elasticity and the effective elastic behaviour of polycrystalline materials: Theory, measurement and computation, Modell. Simul. Mater. Sci. Eng., 7 (1999), 909.
17. S. Vedantam and B. S. V. Patnaik, Efficient numerical algorithm for multiphase field simulations, Phys. Rev. E, 73 (2006), 016703.
18. Y. Ni and M. Chiang, Prediction of elastic properties of heterogeneous materials with complex microstructures, J. Mech. Phys. Solids, 55 (2007), 517.