Foam topology: bending versus stretching dominated architectures

Cellular solids can deform by either the bending or stretching of the cell walls. While most cellular solids are bending-dominated, those that are stretching-dominated are much more weight-efficient for structural applications. In this study we have investigated the topological criteria that dictate the deformation mechanism of a cellular solid by analysing the rigidity (or otherwise) of pin-jointed frameworks comprising inextensional struts. We show that the minimum node connectivity for a special class of lattice structured materials to be stretching-dominated is 6 for 2D foams and 12 for 3D foams. Similarly, sandwich plates comprising of truss cores faced with planar trusses require a minimum node connectivity of 9 to undergo stretching-dominated deformation for all loading states.