Computational Physics Group

Karel Matous










Third-Order Model of Thermal Conductivity for Random Polydisperse Particulate Materials using Well-Resolved Statistical Descriptions from Tomography

A. Gillman and K. Matous

Department of Aerospace and Mechanical Engineering
University of Notre Dame
Notre Dame, IN, 46556, USA.


    For heterogeneous materials, obtaining an accurate statistical description has remained an outstanding problem. We accurately evaluate the three-point microstructural parameter that arises in third-order bounds and approximations of effective material properties. We propose new adaptive methods for computing n-point probability functions obtained from three-dimensional microstructures. We show that for highly packed systems our methods result in a 45% accuracy improvement compared to the latest techniques, and third-order approximations agree well with simulation data. Furthermore, third-order estimates of the effective behavior are computed for tomographically characterized systems of highly filled polydisperse ellipsoids and cuboids for the first time.


    In conclusion, we have demonstrated that effective properties of highly filled random polydisperse particulate systems can be computed with unprecedented accuracy from rich three-dimensional microstructural data. We have described novel adaptive methods for computing third-order bounds and approximations of the effective thermal conductivity for polydisperse composites. With these techniques, proper assessment of the rich mathematical history in computing effective material properties including diffusivity, magnetic and fluid permeability, etc. is now realizable. Furthermore, extension to a wide array of particle types including any Platonic or Archimedean solid is now possible. As random and heterogeneous many-body systems are common in several fields, use of these statistical characterization techniques has wide ranging application in physics, e.g. molecular arrangements, celestial configurations, and beyond.

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2014 Notre  Dame  and Dr. Karel Matous