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Inverse homogenization - Recovery of the structure of composite materials
by
Elena Cherkaev
University of Utah
The talk deals with inverse homogenization problem which is a problem of deriving information about the microgeometry of 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 of two-component composite. This representation relates the n-point correlation functions of the microstructure to the moments of the spectral measure, which contains all information about the microgeometry. The problem of identification of the spectral function from effective measurements in an interval of frequency has a unique solution, however the problem is ill-posed. The talk discusses several stabilization techniques and Pade approximations that could be used for reconstruction of the spectral function. Equivalency of composites' structures is addressed and construction of corresponding finite difference equation using Jacobi matrix is shown. The reconstructed spectral function can be used to recover microstructural parameters and to compute other effective properties of the same composite.
Date received: February 15, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caws-45.