Workshop NanoMath 2014 [610091]
Workshop NanoMath 2014
Zaragoza, October 1{3, 2014
Multiscale Analysis of Nanocomposite Materials
Claudia Timofte
Our goal in this talk is to present some homogenization results for nanocomposite
structures. The fast growing interest in nanotechnology is challenging the scientific
community to study and design new nanocomposite materials for possible applications
in electronics, photonics, computer science, biology, etc. The properties of nanocom-
posite materials are very often superior to those of conventional materials. They
might exhibit increased strength, reduced elastic modulus, reduced density, enhanced
diffusivity, higher electrical resistivity, lower thermal conductivity, increased specific
heat and better magnetic properties compared to classical coarse grained materials.
Combining a multiscale modeling strategy with computational techniques, scientists
try to bridge the different length scales, shedding light on the fundamental mecha-
nisms that determine how such materials behave.
Many properties of nanocomposite materials are associated with interface effects.
A fundamental question is how to predict the effective properties of such a complicated
structure from the properties and the geometry of the individual phases and the
interphase interactions. Via the periodic unfolding method, we shall analyze the
influence of interfaces on the effective thermoelastic properties of some nanocomposite
materials with imperfect interfaces.
We shall also discuss a macroscopic model for semiconductor devices, which are
ubiquitous in the modern computer and telecommunications industry.
In the last part of this talk, we shall focus on a discrete homogenization technique
for a graphene sheet. Via the Γ-convergence method, an equivalent continuuum model
for such a lattice structure is obtained.
This talk is based on joint work with J. I. D´ ıaz and H. I. Ene.
Keywords: homogenization, imperfect interfaces, nanocomposite materials.
Mathematics Subject Classi cation 2000: 35B27, 74M15.
Faculty of Physics
University of Bucharest
P.O. Box MG-11, Bucharest, Romania
[anonimizat]
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