Symmetry-breaking transitions in equilibrium shapes of coherent precipitates

Jog, CS and Sankarasubramanian, R and Abinandanan, TA (2000) Symmetry-breaking transitions in equilibrium shapes of coherent precipitates. In: Journal of the Mechanics and Physics of Solids, 48 (11). pp. 2363-2389.

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Abstract

We present a general approach for determining the equilibrium shape of isolated, coherent, misfitting particles by minimizing the sum of elastic and interfacial energies using a synthesis of finite element and optimization techniques. The generality derives from the fact that there is no restriction on the initial or final shape, or on the elastic moduli of the particle and matrix, or on the nature of misfit. The particle shape is parametrized using a set of design variables which are the magnitudes of vectors from a reference point inside the particle to points on the particle/matrix interface. We use a sequential quadratic programming approach to carry out the optimization. Although this approach can be used to find equilibrium shapes of three-dimensional (3D) particles, we have presented the details of our formulation for two-dimensional systems under plane strain conditions. For systems with cubic elastic anisotropy, the equilibrium shapes and their size dependence are analyzed within the framework of symmetry-breaking shape transitions. For systems with dilatational misfit, our results on shape transitions are in agreement with those in the literature. For systems with non-dilatational misfit, we obtain a symmetry-breaking shape transition that involves a loss of mirror symmetry normal to the x- and y-axes; small particles have this symmetry, while those beyond a critical size do not. With these results, we now have a comprehensive picture of symmetry-breaking transitions in two-dimensional systems driven by anisotropy in misfit and elastic modul.

Item Type:	Journal Article
Publication:	Journal of the Mechanics and Physics of Solids
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elseveir Science.
Keywords:	Inclusions;Anisotropic material;Inhomogeneous material;Finite elements;Optimization
Department/Centre:	Division of Mechanical Sciences > Materials Engineering (formerly Metallurgy) Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	19 Nov 2009 06:10
Last Modified:	22 Feb 2012 08:26
URI:	http://eprints.iisc.ac.in/id/eprint/18283

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