1,016 research outputs found
Homogenization of high-contrast and non symmetric conductivities for non periodic columnar structures
In this paper we determine, in dimension three, the effective conductivities
of non periodic high-contrast two-phase cylindrical composites, placed in a
constant magnetic field, without any assumption on the geometry of their cross
sections. Our method, in the spirit of the H-convergence of Murat-Tartar, is
based on a compactness result and the cylindrical nature of the microstructure.
The homogenized laws we obtain extend those of the periodic fibre-reinforcing
case of [M. Briane and L. Pater. Homogenization of high-contrast two-phase
conductivities perturbed by a magnetic field. Comparison between dimension two
and dimension three. J. Math. Anal. Appl., 393 (2) (2012), 563 -589] to the
case of periodic and non periodic composites with more general transversal
geometries.Comment: 28 page
Bounds on strong field magneto-transport in three-dimensional composites
This paper deals with bounds satisfied by the effective non-symmetric
conductivity of three-dimensional composites in the presence of a strong
magnetic field. On the one hand, it is shown that for general composites the
antisymmetric part of the effective conductivity cannot be bounded solely in
terms of the antisymmetric part of the local conductivity, contrary to the
columnar case. So, a suitable rank-two laminate the conductivity of which has a
bounded antisymmetric part together with a high-contrast symmetric part, may
generate an arbitrarily large antisymmetric part of the effective conductivity.
On the other hand, bounds are provided which show that the antisymmetric part
of the effective conductivity must go to zero if the upper bound on the
antisymmetric part of the local conductivity goes to zero, and the symmetric
part of the local conductivity remains bounded below and above. Elementary
bounds on the effective moduli are derived assuming the local conductivity and
effective conductivity have transverse isotropy in the plane orthogonal to the
magnetic field. New Hashin-Shtrikman type bounds for two-phase
three-dimensional composites with a non-symmetric conductivity are provided
under geometric isotropy of the microstructure. The derivation of the bounds is
based on a particular variational principle symmetrizing the problem, and the
use of Y-tensors involving the averages of the fields in each phase.Comment: 21 page
Mechanics of Micro- and Nano-Size Materials and Structures
For this reprint, we intend to cover theoretical as well as experimental works performed on small scale to predict the material properties and characteristics of any advanced and metamaterials. New studies on mechanics of small-scale structures such as MEMS/NEMS, carbon and non-carbon nanotubes (e.g., CNTs, Carbon nitride, and Boron nitride nanotubes), micro/nano-sensors, nanocomposites, macrocomposites reinforced by micro-/nano-fillers (e.g., graphene platelets), etc., are included in this reprint
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