THE HIERARCHY OF MICROSTRUCTURES FOR LOW-DENSITY MATERIALS

The elastic mechanical behavior for low density materials is examined in both the two dimensional and three dimensional cases. In the 2-D ca se a hierarchy of microstructures are found in which (i) both isotropi c properties are governed by direct material resistance from the cell wall members (ii) a hybrid case in which one of the properties is cont rolled by direct resistance, but the other property is governed by ben ding resistance of the material members and (iii) both properties are controlled by bending resistance. The knowledge of the third case is e ntirely new and the associated microstructure is composed of star shap ed cells. The corresponding 3-D behaviors for the hierarchy of cell ty pes are found through a 3-D orientational averaging procedure.