The main research emphasis of our
laboratory is on the development of mathematically rigorous techniques
for the computational design and control of materials processes
including deformation, solidification and crystal growth processes. Our
interests lie in understanding and controlling the effects of
microstructure evolution in material properties.
The problems of interest are multiscale and multiphysics in nature
governed by partial differential
equations. In such problems, lack of information at different scales
requires that the problems of interest are posed as stochastic problems.
Understanding uncertainty propagation across length scales
in materials is a key ingredient of our research. Stochastic spectral methods,
sparse-grid collocation approximations, Bayesian inference and information theory
are increasingly used to develop a unified framework for modeling
materials across length scales. We are also very active in interfacing
robust control of continuum systems with information technologies
including machine learning techniques in order to develop real time
feedback mechanisms for the control of complex materials processes in
the presence of uncertainty.
Material Process Design and Control Problems
of Current Interest
main material process design problems of current interest are
Computational Mathematics Methods Developed
representation of the microstructure of polycrystal materials and
knowledge discovery by statistical exploration of
structure/property/process relations. Abstract representation
of microstructural elements is fundamental for optimizing
First-principle calculations, molecular dynamics, mesoscopic models,
computational thermodynamics, phase field & level set simulation
methods and virtual interrogation of microstructures.
of gradient-based optimization algorithms for the design of multi-stage
metal forming processes as applied to the manufacturing of aircraft
components. Emphasis is given to the control of
of the effect of various thermo-physical processes on the obtained
crystal structure in the crystal growth of metallic, semiconductor and
organic materials. Current emphasis is given in addressing melt flow
control via optimal furnace design and using non-uniform externally
applied magnetic fields.
of solidification on substrates and optimal design of mold surface
topographies in directional (chill) and continuous casting processes
that lead to desired shell surface topologies and near-surface
of information technologies for the real time control of solidification
sample of recent computational methods developed by the MPDC group
include those listed below.
- Spectral and sparse grid collocation methods
for solving SPDEs in high-dimensions.
- Manifold learning techniques for non-linear data-driven
learning (machine learning) techniques for exploring material databases.
- Stochastic variational
multiscale methods for modeling thermal and flow transport in random heterogeneous media.
- Multiscale estimation using
modeling of the deformation of heterogeneous materials.
sensitivity methods for the computational design of multiscale deformation
set methods for modeling dendritic solidification in the presence of
- Ab initio based multibody energy expansions for
structure and property prediction of alloys.
optimization and adjoint techniques for the control of complex flow and
thermal transport processes.