Computational Physics GroupKarel Matous |
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Third-order Thermo-mechanical Properties for Packs of Platonic Solids Using Statistical Micromechanics
1Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN, 46556, USA. 2Department of Aerospace Engineering University of Illinois Urbana, IL, 61801, USA. 3Department of Aerospace and Mechanical Engineering University of Florida Gainesville, FL, 32611, USA. Abstract
Obtaining an accurate higher order
statistical description of heterogeneous materials and
utilizing this information to predict effective
material behavior with high fidelity has remained an
outstanding problem for many years. In a recent
letter, Gillman and Matous (Gillman and Matous, Physics
Letters A, 378(41), 2014) 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 solids packs using
third-order statistical micromechanics. Systems of
impenetrable and penetrable spheres are considered to
verify adaptive methods for computing n−point
probability functions directly from threedimensional
microstructures, and excellent agreement is shown with
simulation. Moreover, a significant shape effect is
discovered for the effective thermal conductivity of
highly packed composites, while a moderate shape
effect is exhibited for the elastic constants.
Conclusions
Authors’ contributions AG developed the numerical integration/interpolation and statistical sampling methods, conducted numerical experiments and performed subsequent analysis of results. GA and TJ developed the packing algorithm for Platonic solids. KM conceived and coordinated the studies, and contributed to analysis of results. AG and KM drafted the manuscript. All authors approved manuscript for publication. Download the paper here © 2015 Notre
Dame and Dr. Karel Matous
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