A study was undertaken of the mode of failure of open- or closed-cell
cellular materials depending on the variation of the relative density
of the material due to swelling or variation of its porosity. Cellular
materials or foams were considered as transversely isotropic, an assu
mption which corresponds well with their mechanical behaviour. Using a
tenser failure polynomial criterion, and as such the elliptic parabol
oid failure criterion was considered, for the study of the mode of fai
lure of closed-cell foams of different relative densities, it was esta
blished that the failure behaviour of the swelled material drastically
changes its failure mode by becoming a strong tension material from a
strong compression one. Furthermore, there is a critical value of the
relative density for each material, where the substance passes throug
h a quasi-isotropic state and the foam behaves like an isotropic mater
ial, where triaxiality phenomena are insignificant.