Katz J I, Hoffman J J, Conradi M S, Miller J G
Department of Physics and McDonnell Center for the Space Sciences, Washington University, St. Louis, Missouri 63130, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061923. doi: 10.1103/PhysRevE.85.061923. Epub 2012 Jun 25.
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.
我们构建了一种由通过直细杆连接的随机分布节点组成的材料的有效介质（平均场）理论，这些节点通过铰链连接。通过定义与波长相关的有效弹性模量，我们计算了超声纵波和横波的静态模量以及色散关系。在有限波矢k处，波是色散的，相速度和群速度随着波矢的增加而减小。这些结果直接适用于具有空孔隙空间的网络。它们还描述了充满流体的多孔介质的双组分（比奥）理论中的固体基质。我们提出了存在低密度材料的可能性，这些材料的刚度和强度与密度之比高于泡沫、气凝胶或松质骨。
