Skip to main content Accessibility help

A Spectral Iterative Method for the Computation of Effective Properties Of Elastically Inhomogeneous Polycrystals

  • Saswata Bhattacharyya (a1), Tae Wook Heo (a1), Kunok Chang (a1) and Long-Qing Chen (a1)


We report an efficient phase field formalism to compute the stress distribution in polycrystalline materials with arbitrary elastic inhomogeneity and anisotropy The dependence of elastic stiffness tensor on grain orientation is taken into account, and the elastic equilibrium equation is solved using a spectral iterative perturbation method. We discuss its applications to computing residual stress distribution in systems containing arbitrarily shaped cavities and cracks (with zero elastic modulus) and to determining the effective elastic properties of polycrystals and multilayered composites.


Corresponding author



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



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed