Principal Investigator Mark Knackstedt Project s29

Applied Maths, Machine VP

Research School of Physical Sciences and Engineering

Co-investigators: X. Zhang, Applied Maths, Research School of Physical Sciences and Engineering, Prof. M. Sahimi, Chemical Engineering, University of Southern California, U.S.A., Prof. D.Y.C. Chan, Mathematics, University of Melbourne. Lincoln Paterson, CSIRO Petroleum Resources. Prof. W.V. Pinczewski, Petroleum Engineering, Univ. of NSW. Prieur DuPlessis, Applied Maths, U. of Stellenbosch, South Africa. Prof. S.F. Cox, Geology Department, U. of Newcastle

Mechanical and Transport Properties of Model Bicontinuous Materials

Disordered materials abound in nature and in man-made situations. Examples include ceramic composites, geologic media, polymer blends, foams and colloidal dispersions. The determination of effective properties (e.g., conduction, hydraulic transport, mechanical) of disordered composite materials is a subject of great importance in science and engineering. The microstructure of these materials is often quite complex and may possess intricate topology. The macroscopic (observable) transport properties of disordered materials are generally sensitive to the details of the microstructure. An important aspect of theoretically understanding the macroscopic behaviour of such media is to be able to generate and characterise suitable model microstructures.

What are the basic questions addressed?

We are studying the effect of microstructure on the effective properties of composite materials.

What are the results to date and future of the work?

A general model for microstructure was recently proposed by Berk. The model is based on level cuts of a Gaussian random field with arbitrary spectral density. The freedom in specifying the parameters of the model allows the modelling of physical materials with diverse morphological characteristics. We have shown that the model qualitatively accounts for the principal features of a wider variety of disordered materials including geologic media, membranes, polymer blends, ceramics and foams. Correlation functions are derived for the model microstructure. From this characterisation we derive mechanical and conductive properties of the materials. Excellent agreement with experimentally measured properties of disordered solids is obtained. The agreement provides a strong hint that it is now possible to correlate effective physical properties of porous solids to microstructure.

What computational techniques are used and why is a supercomputer required?

The algorithms used to calculate the random field and simulate the effective conductivity were developed in consultation with Dr. David Singleton of the ANUSF. The CMSSL Fortran library is employed in key areas of the implementation. Furthermore the algorithm has been compared with theoretical results for simple geometries and found to perform very well.


A.P. Roberts and M. Teubner, Phys. Rev. E, 51, 4141-4154 (1995).

Mechanical and transport properties of model foamed solids Journal of Materials A.P. Roberts and M.A. Knackstedt, Science Letters, 14, 1357-1359 (1995).