Commun. Comput. Phys., 11 (2012), pp. 726-738.


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

Saswata Bhattacharyya 1*, Tae Wook Heo 1, Kunok Chang 1, Long-Qing Chen 1

1 Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA.

Received 29 June 2010; Accepted (in revised version) 6 April 2011
Available online 28 October 2011
doi:10.4208/cicp.290610.060411a

Abstract

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.

AMS subject classifications: 74B10, 74S25
Key words: Elasticity, spectral method, iterative method.

*Corresponding author.
Email: sxb57@psu.edu (S. Bhattacharyya), tuh134@psu.edu (T. W. Heo), kuc142@psu.edu (K. Chang), lqc3@psu.edu (L.-Q. Chen)
 

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