Computational materials science : the simulation of materials microstructures and properties
The recent advance of numerical prediction methods in nearly all domains of materials
science and engineering has established a new, exciting, interdisciplinary approach which
is often referred to as “computational materials science”. It brings together elements from
materials science, physics, computer science, mathematics, chemistry, and mechanical engineering.
For instance, simulations in the field of materials physics concentrate on the
investigation of lattice and defect dynamics at the atomic scale using molecular dynamics
and Monte Carlo methods. Materials-related simulations in the field of mechanical engineering
focus on large-scale construction problems, using finite element methods where
the microstructure is incorporated by using averaging constitutive laws. In contrast to
these examples, the classical domain of materials science can be seen in the investigation
of lattice defects and their interactions at the mesoscale. Performing simulations
on this particular scale is a great challenge, in that it must bridge enormous space and
time scales and provide concepts to describe adequately complex many-body interaction
phenomena. For this purpose a variety of new concepts has been developed which enables
one to handle the interaction of many individual lattice defects in a more or less
discrete manner at dimensions above the atomic scale and below the macroscopic scale.
These so-called mesoscale simulation methods include deterministic and probabilistic cellular
automata with global and local transformation rules, Ginzburg–Landau-type phase
field kinetic methods, dislocation dynamics, polycrystal and non-linear crystal plasticity
finite element models, geometrical and component models, topological network or vertex
models, and multistate kinetic Potts-type Monte Carlo approaches. However, classical
techniques such as molecular dynamics, Metropolis Monte Carlo, and conventional finite
element simulations are also used extensively.
Although an increasing body of excellent conference proceedings, monographs, and
journals are available covering particular aspects of computational materials science, no
comprehensive overview of that field exists (see General Reading). This contribution aims
to fill that gap. It gives a review of modern approaches to the space- and time-discretized
simulation of materials microstructures, together with the respective theoretical backgrounds,
that currently prevail in materials science. Particular emphasis is placed on the
fundamentals of space- and time-discretized simulations of materials microstructures at
the mesoscale.
The book comprises five Parts. Part I is entitled Introduction and Fundamentals.
After the Introduction it concentrates on aspects which are scale-independent, namely,
definitions and notions used in modeling and simulation, and fundamentals of solving
differential equations. The sequence of the ensuing Parts reflects the spatial and temporal
hierarchy of microstructure, i.e., it presents simulation methods at the nanoscopic–microscopic
(Part II), microscopic–mesoscopic (Part III), and mesoscopic–macroscopic levels
(Part IV). The last chapter provides a review of integrated, i.e., of scale-bridging, modeling
and simulation (Part V). Part II (on the nano–micro level) focuses on the various
Metropolis Monte Carlo and molecular dynamics approaches. Part III (on the micro–
meso level) concentrates on dislocation dynamics, Ginzburg–Landau-type diffuse phase
field kinetic methods, cellular automata, multistate and kinetic Potts models, geometrical
and component models, and topological network and vertex models. Part IV (on the
meso–macro level) presents large-scale finite element and finite difference and polycrystal
models. The chapters are complemented by a discussion of typical applications in the
field of materials science and representative examples.
Due to the fact that it is particularly those simulations that predict microstructure
evolution and microstructure–property relations at the micro–mesoscale, the theoretical
concepts and methods in Part III are discussed in greater detail and furnished with elementary
examples from plasticity, recrystallization and grain growth phenomena, solid-state
diffusion, and phase transformation.
The Appendices present a list of suggested general reading, some basic aspects of
computer science, advanced empirical techniques such as fuzzy logic and artificial neuronal
networks, and a brief introduction to percolation theory.
The book addresses students at the graduate and undergraduate levels, lecturers,
materials scientists and engineers, as well as materials-oriented physicists, chemists, mathematicians,
and mechanical engineers. Any offer of criticism, advice, or example that
might help to improve this text will be highly appreciated.
This book was written during my time at the Institut f¨ur Metallkunde und Metallphysik
at Rheinisch-Westf¨alische Technische Hochschule Aachen and at the Department
of Materials Science and Engineering at Carnegie Mellon University in Pittsburgh. My
warmest thanks are due to my mentors Prof. Dr. G. Gottstein and Prof. Dr. Dr. h.c. K.
L¨ucke, who have steadily promoted and profoundly stimulated my work. I am particularly
indebted to Prof. Dr. H. Mughrabi, Prof. Dr. D. J. Srolovitz, Dr. U. F. Kocks, and
Prof. Dr. A. D. Rollett for discussions and a number of helpful comments. Furthermore, I
am grateful to Prof. Dr. D. M. Barnett, Prof. Dr. M. Berveiller, Prof. Dr. W. Blum,
Prof. Dr. Y. Br′echet, Prof. Dr. U. Glatzel, Dr. P. Gumbsch, Prof. Dr. J. P. Hirth,
Prof. Dr. P. Neumann, Prof. Dr. W. Mao, Prof. Dr. H. Mecking, Dr. D. R¨onnpagel, the
late Prof. Dr. J. Schlipf, Prof. Dr. S. Schmauder, Prof. Dr. L. Shvindlerman, Prof. Dr. Z.
Sun, Prof. Dr. L. T′oth, and Prof. Dr. P. van Houtte for stimulating discussions and fruitful
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