Data Mining and Reduced order
methods for Materials design
Considering the computational complexity involved in multi-length
scale formula-
tions involving polycrystal plasticity, innovative algorithms need to
be incorporated
in techniques for designing processes to realize materials with
optimized properties.
This work demonstrates the synergy between classification of FCC
polycrystal tex-
ture and multi-scale process design for achieving desired properties in
such materials.
The inverse problem of designing processing stages that lead to a
desired texture
or texture-dependent property is addressed by mining over a database of
orienta-
tion distribution functions (ODFs). Given a desired ODF, the
hierarchical classifier
matches its ODF features in the form of pole density functions of
important ori-
entation fibers to a class of textures in the database. Texture classes
are affiliated
with processing information, hence, enabling identification of multiple
process paths
that lead to a desired texture. The process parameters identified by
the classifier are
fine-tuned using a gradient optimization algorithm driven by continuum
sensitivity
analysis of texture evolution. An adaptive reduced-order model for
texture evolution
based on proper orthogonal decomposition is employed in which the
reduced ODF
modes corresponding to the intermediate stages of the design process
are adaptively
selected from the database.
- V. Sundararaghavan and N. Zabaras, "A data mining approach for the design of polycrystalline materials", presented in the symposium `Computational Aspects of Mechanical Properties of Materials: Meso-Scale and Continuum Modeling' (Kwai S. Chan and Diana Farkas, organizers), in the proceedings of EPD Congress 2005, TMS (The Minerals, Metals & Materials Society), 2005 TMS Annual Meeting & Exhibition, San Francisco, CA, February 13-17, 2005. [PPT]
- V. Sundararaghavan and N. Zabaras, "On the synergy between texture classification and deformation process sequence selection for the control of texture-dependent properties" Acta Materialia, Vol. 53(4), pp.1015-1027, 2005.[PDF]
Microstructure
reconstruction
Reconstruction of
three-dimensional (3D) microstructures is posed
and solved as a
pattern recognition problem. A microstructure database is used within a
support
vector machines framework for predicting 3D reconstructions of
microstructures
using limited statistical information available from planar images.
The pattern recognition technique discussed uses two-dimensional
microstructure
signatures to generate in nearly real-time 3D realizations, thus
accelerating predic-
tion of material properties and contributing to the development of
materials-by-
design.
V. Sundararaghavan, N. Zabaras, "Classification of three-dimensional
microstructures using support vector machines", Computational Materials
Science, Vol. 32, pp. 223-239, 2005.[PDF]
Microstructure
representation
Representation
of features from sectional images of microstructures is fundamental to
determining the microstructural influences on material behavior.
Geometric data extracted from planar materialographic sections through
image analysis techniques are primarily lower-order descriptors of the
microstructure. Such descriptors do not contain complete morphological
information and hence cannot fully describe the material
microstructure. This work uses a multi-class support vector machine
classification method in conjunction with principal component analysis
to build a dynamic and evolving microstructure library that can be used
to efficiently describe single-phase polyhedral microstructures.
Lower-order descriptors are initially used to associate the material
microstructure to classes of microstructures stored in a digital
material library. Complete description is obtained by quantifying the
microstructure using the coefficients of a continuously updating basis
within a class of the library. These techniques are essential towards
the development of a dynamic materials library that will be able to
analyze, classify and represent microstructures for modeling,
accelerating the design and testing of single-phase polycrystalline
materials.
V. Sundararaghavan, N. Zabaras, "A
dynamic material library for the representation of single phase
polyhedral microstructures", Acta Materialia, Vol. 52/14, pp.
4111-4119, 2004.[PDF]
V. Sundararaghavan and N. Zabaras, "Representation and classification of microstructures using statistical learning techniques", in the proceedings of NUMIFORM, the 8th International Conference on Numerical Methods in Industrial Forming Processes (edt. S. Ghosh), Columbus, Ohio, June 13-17, 2004. AIP Conference Proceedings 712, 98 (2004).[PPT]