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Updated: May 18, 2026

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
Published on: April 25, 2019
Effective-medium theory of elastic waves in random networks of rods
J I Katz1, J J Hoffman, M S Conradi
1Department of Physics and McDonnell Center for the Space Sciences, Washington University, St. Louis, Missouri 63130, USA. katz@wuphys.wustl.edu
Abstract:
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.
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