| Three--dimensional cellular materials are ubiquitous in nature and are also used in a variety of engineering applications, ranging from sandwich structures with low density cores for structural protection, sound and thermal insulation, and heat transfer to scaffolds for tissue engineering and regenerative medicine. In many of these applications, the mechanical properties and structural behavior of the cellular materials play a key role in regulating the overall function of the system.;In this work, a series of analytical relationships is presented to predict the mechanical properties and response of open three--dimensional Voronoi tessellation of faced--centered cubic structures called rhombic dodecahedrons. The cell edge material was assumed to be elastic--perfectly plastic and the effective mechanical properties of the cellular structure were related to the cell edge material properties and the relative density of the cellular structure. Detailed finite element models were carried out to establish the validity of the analytical models. In the elastic regime, the monodisperse cellular structure is orthotropic and near--incompressible in all loading directions and its response is governed by bending deformation of the cell edges. However, the yield strength of the cellular structure in all loading directions is qual. In the next part of the work, we studied the role of irregularity in the organization of the cellular structure on its mechanical properties. The irregularity in the cellular structure organization was introduced by moving the vertices of a regular cellular structure in three orthogonal directions by a random value within a predefined range called the "Irregularity index". At a constant overall relative density, increasing the level of irregularity increases the effective elastic modulus, and significantly decreases the effective yield strength of the cellular structure. We also studied the mechanical properties of the open and closed cellular structures tied to rigid plates, in view of the application of cellular structure as the core construction of sandwich panels. In this case, the cellular structure is significantly stiffer and its mechanical response is dominated by cell wall stretching. |
