title: Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics.
abstract: Obtaining an accurate higher order statistical description of heterogeneous materials and using this information to predict effective material behaviour with high fidelity has remained an outstanding problem for many years. In a recent letter, Gillman & Matouš (2014Phys. Lett. A378, 3070-3073. ()) accurately evaluated the three-point microstructural parameter that arises in third-order theories and predicted with high accuracy the effective thermal conductivity of highly packed material systems. Expanding this work here, we predict for the first time effective thermo-mechanical properties of granular Platonic solid packs using third-order statistical micromechanics. Systems of impenetrable and penetrable spheres are considered to verify adaptive methods for computingn-point probability functions directly from three-dimensional microstructures, and excellent agreement is shown with simulation. Moreover, a significant shape effect is discovered for the effective thermal conductivity of highly packed composites, whereas a moderate shape effect is exhibited for the elastic constants.
authors.affiliation: Department of Aerospace and Mechanical Engineering , University of Notre Dame , Notre Dame, IN 46556, USA.
authors.forename: A
authors.initials: A
authors.lastname: Gillman
authors.affiliation: Department of Aerospace Engineering , University of Illinois , Urbana, IL 61801, USA.
authors.forename: G
authors.initials: G
authors.lastname: Amadio
authors.affiliation: Department of Aerospace and Mechanical Engineering , University of Notre Dame , Notre Dame, IN 46556, USA.
authors.forename: K
authors.initials: K
authors.lastname: Matouš
authors.affiliation: Department of Aerospace and Mechanical Engineering , University of Florida , Gainesville, FL 32611, USA.
authors.forename: T L
authors.initials: TL
authors.lastname: Jackson
keywords: adaptive interpolation/integration; effective material properties; heterogeneous materials; high-performance computing; statistical micromechanics