Qiang's Research Gallery 7
Computational Materials Sciences
Recent advances in both computational materials science and
information technology during the last two decade have led to a
paradigm shift for materials development towards the materials
by computational design approach which promises to not only save
cost but also accelerate the insertion of new materials to
A critical component in the materials by
computational design framework is the computational prediction of
material microstructures under different processing conditions,
i.e., compositional and structural inhomogeneities, which
essentially control the physical and mechanical properties of a
Recently, we have been designing fast, robust and
adaptive algorithms for the solution of
a variety of applications problems in materials sciences.
Our efforts include the study of:
- Multi-scale materials simulation and design
At Penn State, we have been working with a number of
colleagues in materials sciences on the
multi-scale materials simulation and design, which is
the theme of our five-year $2.9million NSF sponsored ITR
and also our research within the NSF-IUCRC PennState/GaTech
Center for Computational Materials
- Diffuse interface/phase field modeling and simulations
Diffuse interface/phase field method is very popular in
computational materials science. The idea goes back to van de Walls
more than 100 years ago.
Much of our works have followed from
the pioneering works of Cahn and Hilliard for phase transition problems.
A smooth order parameter is used to define the material interface/defects
implicitly which has a thin (but finite) transition layer across the
interface. The approach enjoys the same spirit as the
Ginzburg-Landau formalism for the
mesoscopic modeling of superconductivity and quantized vortices.
- Critical nuclei morphology in solid state transformations
Nucleation is an important problem in materials sciences.
We recently developed a diffuse interface method for predicting the critical
nuclei morphology in solid state transformations. For the first time, we
were able to reveal the dependence of possible critical nuclei on the elastic
energy contributions in anisotropic elastic solids. Two-dimensional
energy diagram is shown in a recent PRL paper.
The critical nuclei can be predicted without a priori information
via the computation of saddle point and
minimum energy path.
In 3-d, there are two other possible nuclei branches with lower
the plate shape often has lower formation energy.
- Adaptive spectral methods for phase field methods
Phase field simulation of microstructure evolution is an
important part of the our multiscale materials simulation
process. To improve its performance,
we combine the moving mesh idea with the high resolution and
Fast FFT-based implementation of spectral methods into an
adaptive spectral methods for the phase field models.
A map is used between the computational and physical domain so that the grids still remain uniform in the computational domain,
but the physical mesh becomes clustered near the interfacial regions
and thus provide better resolution.
To minimize the overhead, the moving mesh PDEs are solved in
a similar manner as the original phase field models via
semi-implict integration with time splitting.
The performance of numerical scheme is much
improved with the moving mesh Fourie spectral method when the
microstrucure has concentrated interfacial regions.
- Automated phase diagram computation
Algorithms are developed to compute the correct
phase diagram by automatically identifying the
presence of miscibility gap.
- Simulations of other materials defects and multiscale modeling
- Modeling and simulations of special materials properties
Such as superfluidity, superconductivity, viscoelasticity, ...
List of collaborators: L.Chen, Z. Liu, W. Feng, M. Emelianenko,
P.Yu, S. Hu, L. Zhang
algorithm for the automation of phase diagram calculation,
by M. Emelianenko, Z. Liu and Q. Du,
Materials Sciences, 35, pp.61-74, 2006.
Numerical Analysis of
a Continuum Model of Phase Transition,
by Q. Du and R. A. Nicolaides,
SIAM J. Numer. Anal.,
28, No.5, pp1310-1322, 1991;
An integrated Framework for multi-scale materials simulation and design,
by Z. Liu, L. Chen, P. Raghavan, Q. Du, J. Sofo,
S. Langer and C. Wolverton,
J. Computer Aided
Materials Design, 11, pp.183-199, 2004
An iterative-perturbation scheme for treating inhomogeneous elasticity in phase-field models,
by P. Yu, S. Hu, L. Chen and Q. Du,
J. Computational Phys., 208, pp.34-50, 2005
Spectral implementation of an adaptive moving mesh method for phase-field equations
W. Feng, P. Yu, S. Hu, Z. Liu, Q. Du and L. Chen,
J. Computational Phys., 220, pp.498-510, 2006
A Variational Construction of Anistropic Mobility in Phase-Field Simulation,
by P. Yu and Q. Du,
Discrete and Continous Dynamic Systems, 6, pp.391-406, 2006
Applications of Moving Mesh Methods to
the Fourier Spectral Approximations of Phase-Field Equations,
P. Yu, L. Chen and Q. Du,
Recent Advances in Computational Sciences: Selected Papers from
the International Workshop on Computational Sciences and Its Education,
edited by Jorgensen et. al., World Scientific, 2007 (ISBN: 981270700X)
Retrieving Topological Information for Phase Field Models,
by Q. Du, C. Liu and X. Wang, SIAM J. Appl. Math,
65, pp.1913-1932, 2005
Adaptive Finite Element Method for a Phase Field Bending Elasticity Model
of Vesicle Membrane Deformations,
Q. Du and J. Zhang,
SIAM J. Sci. Comp.,
30, no3, pp.1634-1657, 2008
A Fourier Spectral Moving
Mesh Method for the Cahn-Hilliard Equation
W. Feng, P. Yu, S. Hu, Z. Liu, Q. Du and L. Chen,
in Computational Phys., 5, pp. 582-599, 2009
Morphology of critical nuclei in solid state phase
by Lei Zhang, L.Q. Chen and Q. Du,
Physical Review Letters 98, 265703, 2007
Mathematical and numerical aspects of phase-field approach to critical nuclei morphology in solids,
Lei Zhang, L.Q. Chen and Q. Du,
to appear in J. Scientific
Computing, 2008 (special volume to
the 2007 John Barrett Memorial Lectures).
Diffuse-Interface Description of Strain-Dominated Morphology of Critical
Nuclei in Phase Transformations,
L. Zhang, L.Q. Chen and Q. Du,
Materialia, 56, pp.3568-3576, 2008.
- More can be found in the publications