Effective-medium theory of elastic waves in random networks of rods

We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining wavelength-dependent effective elastic moduli, we calculate both the static moduli and the dispersion relations of ultrasonic...

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Bibliographic Details
Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 85; no. 6 Pt 1; p. 061923
Main Authors Katz, J I, Hoffman, J J, Conradi, M S, Miller, J G
Format Journal Article
LanguageEnglish
Published United States 01.06.2012
Subjects
Biopolymers - chemistry
Computer Simulation
Elasticity - physiology
High-Energy Shock Waves
Models, Biological
Models, Chemical
Models, Molecular
Nanotubes - chemistry
Nanotubes - ultrastructure
Scattering, Radiation
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Summary:We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining wavelength-dependent effective elastic moduli, we calculate both the static moduli and the dispersion relations of ultrasonic longitudinal and transverse elastic waves. At finite wave vector k the waves are dispersive, with phase and group velocities decreasing with increasing wave vector. These results are directly applicable to networks with empty pore space. They also describe the solid matrix in two-component (Biot) theories of fluid-filled porous media. We suggest the possibility of low density materials with higher ratios of stiffness and strength to density than those of foams, aerogels, or trabecular bone.
ISSN:1550-2376
DOI:10.1103/PhysRevE.85.061923