Introduction and synopsis

The structure of cells has fascinated natural philosophers for at least 300 years. Hooke examined their shape, Kelvin analysed their packing, and Darwin speculated on their origin and function. The subject is important to us here because the properties of cellular solids depend directly on the shape and structure of the cells. Our aim is to characterize their size, shape and topology: that is, the connectivity of the cell walls and of the pore space, and the geometric classes into which these fall.

The single most important structural characteristic of a cellular solid is its relative density, ρ*/ρs (the density, ρ*, of the foam divided by that of the solid of which it is made, ρs). The fraction of pore space in the foam is its porosity; it is simply (1 — ρ*/ρs). Generally speaking, cellular solids have relative densities which are less than about 0.3; most are much less – as low as 0.003. At first sight one might suppose that the cell size, too, should be an important parameter, and sometimes it is; but (as later chapters show) most mechanical and thermal properties depend only weakly on cell size. Cell shape matters much more; when the cells are equiaxed the properties are isotropic, but when the cells are even slightly elongated or flattened the properties depend on direction, often strongly so. And there are important topological distinctions, too.