Periodic cellular metals (PCM) are highly porous structures with 20% or less of their interior volume occupied by metal. Some, such as hexagonal honeycomb, are widely used to enable the design of light weight sandwich panel structures, for creating unidirectional fluid flows, for absorbing the energy of impacts, to impede thermal transport across the faces of sandwich panels and for acoustic damping. Corrugated (prismatic) metals are also a form of periodic cellular metal structure. They have their voids arranged in one direction enabling fluid flow in one direction but not the others. They are widely used in building and ship construction and for cross flow heat exchangers. More recently, significant interest has emerged in lattice structures which have 3-D interconnected void spaces well suited for allowing fluid flow through them. The structures of interest here are composed of repeating unit cells with cell diameters that range from tens of micrometers to tens of millimeters.

Honeycomb Structures
Honeycomb structures are composed of plates or sheets that form the edges of unit cells. These can be arranged to create triangular, square, hexagonal or related shapes. Their unit cells are repeated in two dimensions to create a cellular solid, Figure 1. One of the manufacturing methods used to create hexagonal honeycomb leads to a doubling in wall thickness of every other web which results in anisotropic mechanical behavior. All honeycombs are closed cell structures. By identifying a unit cell and deriving the volume fraction occupied by metal, it is possible to obtain simple relations between the relative density where is the density of the cellular structure and is that of the solid from which it is made and the topology of the structure (see Table 1).

Prismatic Structures
If the cores shown in Figure 1 are rotated 90° about their horizontal axis, they become prismatic structures with open (easy flow) cells in one direction and a closed cell structure in the two orthogonal directions. Other prismatic structures are also easy to make. Figure 2 shows three examples. In these figures, the prismatic layers are shown laminated with a 90° in-plane rotation (0/90°) between the layers illustrating the possibility of varying the anisotropy of the structure and enabling the cell size to be made independent of the distance between face sheets when used in sandwich panels. Table 2 shows the relative density - unit cell geometry relations for prismatic cellular structures.

Lattice Truss Structures
Closed cell honeycombs and partially open prismatic structures are constructed from plate or sheet elements. Fully open cell structures can be created from slender beams (trusses) that in principle can be of any cross sectional shape (circular, square, rectangular, I-beam, or hollow). The trusses can be arranged in many different configurations depending upon the intended application. Figures 3 and 4 show six examples of micro truss cellular topologies used as the cores of sandwich panels. Table 3 identifies pertinent unit cells and relative density relationships.

The tetrahedral structure has three trusses each meeting at a face sheet node, whereas the pyramidal structure has four trusses meeting at a face sheet node. In both topologies, the trusses form a continuous network. Both also have directions of unobscured “easy flow”. There are three of these channels in a single layer of the tetrahedral structure and two in the pyramidal system. A slightly different topology is referred to as a 3D Kagomé topology. Kagomé is a Japanese term for the basket weave pattern created by in-plane weaving in three directions. Such 2D weaves have been found to be very strong. In this structure, the nodes that are formed at the face sheets have the 2D Kagomé weave pattern. Pairs of tetrahedrons are inverted and rotationally offset from each other by 60° to create the 3D topology. Each of the three topologies is efficient at supporting structural loads – especially the shear loads encountered in panel bending.

Other lattice truss topologies have also been proposed based upon manufacturing considerations. Figure 4 show examples that are easy to make from wires or tubes. The diamond textile structure is made from layers of a plain weave metal fabric that have been bonded to each other. A simple wire lay up process can be used to create diamond and square truss structures. Their unit cells and relative density relations are also summarized in Table 3.

Tetrahedral/Kagomé	Pyramidal	Diamond Textile	Hollow Diamond

The micro truss topologies shown above are all configured as the cores of sandwich panels. Here in the periodic cellular materials laboratory at the University of Virginia, we have developed numerous manufacturing methodologies for the fabrication of all the these topologies from a variety of materials including, stainless steels, aluminum, copper, nickel and titanium alloys in addition to polymer and metal matrix composites. More information on manufacturing can be found in the PERIODIC CELLULAR MATERIALS: MANUFACTURING section.