title: Effective-medium theory of elastic waves in random networks of rods.
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.
authors.affiliation: Department of Physics and McDonnell Center for the Space Sciences, Washington University, St. Louis, Missouri 63130, USA. katz@wuphys.wustl.edu
authors.forename: J I
authors.initials: JI
authors.lastname: Katz
authors.forename: J J
authors.initials: JJ
authors.lastname: Hoffman
authors.forename: M S
authors.initials: MS
authors.lastname: Conradi
authors.forename: J G
authors.initials: JG
authors.lastname: Miller
mesh_terms: D001704:Biopolymers / Q000737:chemistry*; D003198:Computer Simulation; D004548:Elasticity / Q000502:physiology; D019220:High-Energy Shock Waves; D008954:Models, Biological; D008956:Models, Chemical; D008958:Models, Molecular; D043942:Nanotubes / Q000737:chemistry* / Q000648:ultrastructure*; D012542:Scattering, Radiation
chemical_list: D001704:Biopolymers