|
Research
Overview
Internal structures are at
the heart of the materials science paradigm,
connecting processing to properties and
performance. It is the cumulative interaction of
geometric and crystallographic internal
structures: from nano, micro and meso to macro
scale; that is exhibited in the form of response
of the material. At the nano scale, the problem of
packing objects in space has immense practical
importance in subjects ranging from a study
of the crystal structure of materials, glasses
& liquids to gene & protein folding and
communication theory. At the micron scale the
interaction of grains, sub- domains,
micro-texture, precipitates and other
microstructural features is dominant.
My research interest
encompasses the above length scales to
mathematically model structures and study
materials response and behavior. Specifically, my
research deals with the sub field of
microstructural-mechanics. Microstructural-mechanics
is a modern equivalent of traditional mechanical
metallurgy. It combines the computational methods
of structural mechanics and materials sciences in
a framework defined by heterogeneous materials
microstructure. The success of the above
methodology depends on the mathematical
representation of the materials microstructure.
This becomes particularly more challenging since,
in spite of recent advances in microscopy (SPM,
EBSD, etc.), the microstructural characterization
is limited to 2D surfaces whereas the true
microstructure is three-dimensional in nature.
Thus a main thrust of my research is in
deconvolution of true three-dimensional
microstructure by combining data from various 2D
characterization techniques. This involves study
of mathematical relations on the intersection of
d-dimensional planes through objects in hyperspace
and arrangement & tiling of objects in space.
This is achieved by a combination of integral
geometry, measure theory and mathematical
morphology. It is complemented by high-resolution
microscopy and computer modeling.
|
