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Mogadalai Gururajan's blog

Elastic stress driven phase inversion

Submitted by Mogadalai Gururajan on
research
inhomogeneous elasticity
phase field modelling
microstructural evolution
phase inversion

A typical two phase microstructure consists of a topologically continuous `matrix' phase in which islands of `precipitate' phase are embedded. Usually, the matrix phase is also the majority phase in terms of volume fraction. However, sometimes this relationship between the volume fraction and topology is reversed, and this reversal is known as phase inversion. Such a phase inversion can be driven by an elastic moduli mismatch in two-phase solid systems. In this paper (submitted to Philosophical magazine), we show phase inversion, and the effect of the elastic moduli mismatch and elastic anisotropy on such inversion.

Elastic stress driven rafting

Submitted by Mogadalai Gururajan on
research
phase field modelling
rafting
Ni-base superalloys
microstructural evolution
inhomogeneous elasti

During solid-solid phase transformations elastic stresses arise due to a difference in lattice parameters between the constituent phases. These stresses have a strong influence on the resultant microstructure and its evolution; more specifically, if there be externally applied stresses, the interaction between the applied and the transformation stresses can lead to rafting.

The SIAM 100-digit challenge of Bronemann et al: A review

Submitted by Mogadalai Gururajan on
education
numerical methods
book review
computing

Suppose if somebody asked you the following question, and more importantly, wanted the answer to an accuracy of 100-digits:

  • Problem A: A particle at the center of a 10 x 1 rectangle undergoes Brownian motion (i.e., two-dimensional random walk with infinitesimal step lengths) until it hits the boundary. What is the probability that it hits at one of the ends rather than at one of the sides?


Or, this question (again, demanding the answer to an accuracy of 100-digits):

Some numerical mechanics software

Submitted by Mogadalai Gururajan on
research
Mesh generation
numerical mechanics
distributed computing
data management

Recently, during one of my net searches, I came across this page of RPI, where I learnt about a couple of numerical mechanics software which might be of interest to some of you.

FMDB:

As for the effort toward the scalable engineering simulations on distributed environements, we addressed this challenge by developing a distributed mesh data management infrastructure that satisfies the needs of distributed domain of applications.

Eshelby and his two classics (and some more on the side)

Submitted by Mogadalai Gururajan on
elasticity
inclusions
inhomogeneities
Green function

Eshelby and the inclusion/inhomogeneity problems

Any materials scientist interested in mechanical behaviour would be aware of the contributions of J.D. Eshelby. With 56 papers, Eshelby revolutionised our understanding of the theory of materials. The problem that I wish to discuss in this page is the elastic stress and strain fields due to an ellipsoidal inclusion/inhomogeneity - a problem that was solved by Eshelby using an elegant thought experiment.

In two papers published in the Proceedings of Royal Society (A) in 1957 and 1959 (Volume 241, p. 376 and Volume 252, p. 561) Eshelby solved the following problem ("with the help of a simple set of imaginary cutting, straining and welding operations"): In his own words,

Microstructural evolution in elastically inhomogeneous systems

Submitted by Mogadalai Gururajan on
research
inhomogeneous elasticity
spectral techniques
phase field modelling

I am very happy to be part of iMechanica, and what best way to start than post some stuff that I have been doing recently. I received my PhD for a thesis I submitted to the Department of Materials Engineering (formerly Department of Metallurgy), Indian Institute of Science, Bangalore 560012 INDIA titled Elastic Inhomgeneity Effects on microstructures: a phase field study.

A mismatch in elastic moduli is the primary driving force for certain microstructural changes; for example, such a mismatch can result in rafting, phase inversion, and thin film instability.

My thesis is based on a phase field model, which is developed for the study of microstructural evolution in elastically inhomogeneous systems which evolve under prescribed traction boundary conditions; however, we show that it is also capable of simulating systems which are evolving under prescribed displacements.

The (iterative) Fourier based methodology that we adopt for the solution of the equation of mechanical equilibrium is characterised by comparing our numerical elastic solutions with corresponding analytical sharp interface results; in addition to being accurate, this solution methodology is also very efficient. We integrate this solution methodology into our phase field model, to study microstructural evolution in systems with dilatational misfit.

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