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 case a hierarchy of microstructures are found in which (i) both isotropic properties are governed by direct material resistance from the cell wall members (ii) a hybrid case in which one of the properties is controlled by direct resistance, but the other property is governed by bending resistance of the material members and (iii) both properties are controlled by bending resistance. The knowledge of the third case is entirely new and the associated microstructure is composed of star shaped cells. The corresponding 3-D behaviors for the hierarchy of cell types are found through a 3-D orientational averaging procedure.