Mathematics Colloquium:Inverse homogenization:Identification of information about the structure of composite material..
4:10 p.m. Neill 5W
Abstract: The talk deals with a problem of deriving information about the microstructure of a composite material from its effective properties. The approach is based on reconstruction of the spectral measure in the analytic Stieltjes representation of the effective tensor. The spectral measure contains all information about the microgeometry. The problem of identification of the spectral function from the effective complex permittivity of a two-component random mixture has a unique solution if the permittivity is known in an interval of frequency. However, the problem is ill-posed. We discuss several stabilization techniques that can be used to reconstruct the spectral function. We show results of reconstruction of geometric parameters for a mixture of two materials with different complex permittivity and in a problem of torsion of a heterogeneous beam made of elastic and visco-elastic materials. The reconstructed spectral function can be used to compute other effective properties of the same composite, this gives solution to the problem of coupling of different effective properties of a two-component random mixture.