CSAR Seminar
SPEAKER: Sethuraman Sankaran,
Cornell University
TITLE:
Computational Techniques for Uncertainty Modeling and Robust Design of
Material Systems
DATE: Monday, April 7, 2008
TIME: 12:00 Noon
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
ABSTRACT
As applications of materials continue to increase in complexity, there
is a clear need to assess quantitatively and optimize material
performance in the presence of uncertainties. Insufficient knowledge
of the physical phenomena at different length scales, the lack of
understanding of the way information propagates from one length scale
to another, and the presence of inherent uncertainties lead to material
response that cannot be accurately predicted using deterministic
models. In this work, a novel computational framework for robust
control and design of complex systems is developed. The computational
tools developed in this work include (i) a maximum entropy technique
for accurate modeling of input uncertainties (such as microstructural
geometry and textures for a polycrystalline material) in material
systems using experimental evidence and (ii) a stochastic optimization
algorithm employing a sparse grid stochastic collocation technique for
robust design of complex systems.
The principle of maximum entropy is often used in statistical physics
and provides a reliable strategy for uncertainty modeling in the face
of limited information. Further, a sparse grid stochastic collocation
based technique developed herein shows a remarkable improvement in
computational efficiency compared to conventional Monte-Carlo and
general polynomial chaos expansion (GPCE) techniques. These techniques
are used in conjunction with finite element techniques for simulation
of physical phenomenon in material systems. Several numerical examples
are detailed, including applications to thermal-diffusive systems, flow
in porous media, and uncertainty propagation in polycrystalline
systems.