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Theoretical elastic moduli for disordered packings of interconnected spheres
Alessio Zaccone1, Marco Lattuada, Hua Wu
1Institute for Chemical and Bioengineering, Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland. alessio.zaccone@chem.ethz.ch
The Journal of Chemical Physics
|November 13, 2007
Summary
A new theoretical model provides analytical expressions for elastic moduli in disordered sphere ensembles. This model accurately predicts Young
Area of Science:
- Materials Science
- Solid Mechanics
- Statistical Physics
Background:
- Disordered ensembles of spheres interconnected by physical bonds exhibit complex elastic properties.
- Existing models often struggle to accurately capture the behavior of such systems, particularly concerning surface forces and interparticle interactions.
Purpose of the Study:
- To develop a theoretical model providing analytical expressions for the elastic moduli (Young's, shear, and bulk) of disordered isotropic ensembles of spheres.
- To account for interparticle interactions, including surface forces for rigid and deformable spheres, and Born repulsion energy for colloidal aggregates.
Main Methods:
- Derivation of analytical expressions for Young's and shear moduli based on an ideal random isotropic network and the radial distribution function.
- Development of a theoretical expression for the bulk modulus using an atomistic approach analogous to noble gas solids and colloidal crystals.
- Statistical description of disordered spatial distribution and incorporation of a two-body mean-field interaction potential including Born repulsion energy.
Main Results:
- Analytical expressions for Young's modulus, shear modulus, and bulk modulus of disordered sphere ensembles have been successfully derived.
- The model accounts for different interparticle interaction scenarios, including rigid and deformable spheres, and the crucial role of Born repulsion.
- The derived expressions show consistency with two recent experimental datasets.
Conclusions:
- The developed theoretical model offers accurate predictions for the elastic moduli of disordered isotropic ensembles of spheres.
- The inclusion of specific interaction potentials, like Born repulsion, is essential for describing compression behavior in aggregated systems.
- The model's validity is supported by its agreement with experimental data, providing a valuable tool for understanding disordered materials.
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