Communications in Mathematical Sciences
Volume 14 (2016)
Homogenization of materials with sign changing coefficients
Pages: 1137 – 1154
We investigate a periodic homogenization problem involving two isotropic materials with conductivities of different signs: a classical material and a metamaterial (or negative material). Combining the T-coercivity approach and the unfolding method for homogenization, we prove well-posedness results for the initial and the homogenized problems and we obtain a convergence result. These results are obtained under the condition that the contrast between the two conductivities is large enough in modulus. The homogenized matrix, is generally anisotropic and indefinite, but it is shown to be isotropic and (positive or negative) definite for particular geometries having symmetries.
metamaterials, homogenization, periodic unfolding, T-coercivity, indefinite operators
2010 Mathematics Subject Classification
35B27, 35M99, 35Q60, 78A48, 78M30