# Microstructural evolution in elastically inhomogeneous systems: I. A phase field formulation

Gururajan, MP and Abinandanan, TA (2006) Microstructural evolution in elastically inhomogeneous systems: I. A phase field formulation. [Preprint]

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## Abstract

We present a phase field model suitable for studying phenomena, such as rafting, in which the elastic modulus mismatch (elasticinhomogeneity) plays a central role during microstructural evolution. This model requires a numerical technique for solving for the elastic stress fields in such inhomogeneous systems with, or without an applied stress. We present a technique, adapted from the literature on homogenisation, in which a periodic displacement field ($\mathbf{u}^{\star}$) and a homogeneous strain ($\mathbf {E}$) may be calculated consistent with a given macroscopic applied stress. We also describe an efficient Fourier transform based iterative technique for solving for $\mathbf {u}^{\star}$ and $\mathbf{E}$. We characterise this technique by comparing its results against known analytical results in a variety of settings.

Item Type: Preprint Publisher Phase field modeling;Microstructure;Homogenisation;Thin films;Elastic stress effects Division of Mechanical Sciences > Materials Engineering (formerly Metallurgy) 30 May 2006 22 Feb 2012 08:47 http://eprints.iisc.ernet.in/id/eprint/7063