Reconstructing Complex Materials via Effective Grain Shapes

C. H. Arns, M. A. Knackstedt, and K. R. Mecke
Phys. Rev. Lett. 91, 215506 – Published 21 November 2003

Abstract

We introduce a powerful method based on integral geometry and the Kac theorem for the spectrum of the Laplace operator to define the effective shape of an inclusion in a system made up of a distribution of arbitrarily shaped constituents. Reconstructing the microstructure using the effective inclusion shape leads to an excellent match to the percolation thresholds and to the mechanical and transport properties across all phase fractions. Use of the equivalent shape in effective medium formulations leads to good predictions. The method is verified for a sedimentary rock sample.

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  • Received 16 June 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.215506

©2003 American Physical Society

Authors & Affiliations

C. H. Arns and M. A. Knackstedt

  • Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
  • School of Petroleum Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia

K. R. Mecke

  • Max-Planck-Institut für Metallforschung, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
  • Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

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Issue

Vol. 91, Iss. 21 — 21 November 2003

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