2011/09/20 by Marc Briane, Briane, Marc, Laurent Pater +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems
paper · doi:10.48550/arxiv.1109.4355
openalex publication_date 2011/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Homogenized laws for sequences of high-contrast two-phase non-symmetric conductivities perturbed by a parameter h are derived in two and three dimensions. The parameter h characterizes the antisymmetric part of the conductivity for an idealized model of a conductor in the presence of a magnetic field. In dimension two an extension of the Dykhne transformation to non-periodic high conductivities permits to prove that the homogenized conductivity depends on h through some homogenized matrix-valued function obtained in the absence of a magnetic field. This result is improved in the periodic framework thanks to an alternative approach, and illustrated by a cross-like thin structure. Using other tools, a fiber-reinforced medium in dimension three provides a quite different homogenized conductivity.