This special issue follows a workshop on “Multiscale simulation of heterogeneous materials and
coupling of thermodynamic models”, which was organized at KU Leuven, Belgium on January 1214, 2011. The goal of the workshop was to bring together experts in the fields of multi-scale
thermodynamic modeling and computational multi-scale techniques. Both communities treat the
same phenomena and applications. Nevertheless, they use different approaches and have a
different scientific focus.
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Within a thermodynamic approach, phase-field, CALPHAD and ab initio techniques are
typically coupled to simulate microstructure evolution in multi-component heterogeneous
materials. CALPHAD and phase-field models are based on the formulation of
thermodynamic energy functions, describing the relevant phenomena on the mesoscale. The
coupling with ab initio calculations provides the necessary information for the
thermodynamic energy functions and kinetic coefficients. Here, the focus is on application to
real materials, multi-component and multi-phase systems.
Computational multiscale techniques systematically upscale from smaller to larger spatiotemporal scales using mathematical and physical principles. Widely adopted techniques
include the quasi-continuum method, the use of representative volume elements and other
computational homogenization approaches. Here, the focus is on numerical correctness,
accuracy, stability and efficiency.
The goal of the workshop was, and therefore the goal of this special issue is, actively stimulate
common activities and discussions. The workshop program contained 9 invited speakers, each
giving a lecture of 50 minutes, and 23 contributed speakers, each giving a lecture of 25 minutes.
In total, there were approximately 60 participants. To stimulate interaction between both
communities, presentations from the 2 fields were scheduled alternately. Furthermore, several
social activities were organized, such as a poster evening with cheese and wine. There was large
mutual interest between both communities for each other’s achievements and techniques. The
workshop ended with a general discussion, from which it was clear that collaboration between
both fields would lead to new developments.
This special issue is meant as a stepping-stone to achieve the required cross-fertilization. It
contains contributions from both fields, presented in such a way that they are accessible for both
communities. Especially, each paper was required to have an extensive introduction, and experts
from both communities have reviewed each paper.
There are 4 papers devoted to thermodynamic approaches and alloy systems. In a first paper, A.
Kroupa gives on overview on how thermodynamic properties, such as heat of formation and heat
capacities, and phase diagrams of real multi-component alloys can be predicted using the
CALPHAD approach. Next, there are 2 papers illustrating how different CALPHAD models can
be applied to different types of materials. G. Klančnik and J. Medved consider Al-Sb-Zn alloys,
and L. Zhang and co-authors the oxide system M2O-SiO2. In the paper of N. Barbin and coauthors, a model is presented to calculate the liquid – vapor equilibria for Pb-Bi alloys.
Additionally, there are 5 papers devoted to computational multiscale techniques. In a first paper,
S. Prudhomme and co-authors present a novel force-based scheme for coupling concurrent
local/nonlocal models. Furthermore, two papers deal with simulating the macroscopic response of
materials to deformation. V. Kouznetsova and co-authors consider a computational
homogenization approach in which a macroscopic finite element model is coupled to a
microscopic finite element model resolving the heterogeneous microstructure. J. Gawad and coauthors use a macroscopic finite element model in which the constitutive law is estimated based
on a microscopic model for texture evolution. Finally, two papers deal with coarse-graining of
atomistic models. X. Blanc and F. Legoll consider techniques to obtain macroscopic quantities as
ensemble averages over a large number of atoms, whereas Li and Luskin look at coupling
macroscopic deformation models to a local atomistic model near a lattice instability.
We conclude by expressing our sincere gratitude to our industrial partners (Arcelor Mittal,
Bekaert and Umicore) and the Research Foundation – Flanders (FWO – Vlaanderen, SNR) for
financial support for the organization of this workshop and to the European COST-MP0602
Action “Advanced Solder Materials for High Temperature Application (HISOLD)” for their
support to early-stage researchers to attend this workshop.
The editors,
Nele Moelans, Department of Metallurgy and Materials Engineering, K.U.Leuven
Giovanni Samaey, Numerical Analysis and Applied Mathematics, Department of Computer
Science, K.U.Leuven