A study was undertaken for the mode of failure of open- or closed-cell cellular materials depending on the variation of the relative density of the material because of swelling or variation of its porosity. The cellular materials or foams were considered as transversely isotropic, an assumption which corresponds well with their mechanical behavior. Using a tensor failure polynomial criterion, and as such the elliptic paraboloid failure criterion was considered, for the study of the mode of failure of closed-cell foams of different relative densities, it was established that the failure behavior of the swelled material changes drastically its failure mode by becoming a tension strong material from a compression-strong one. Furthermore, there is a critical value of the relative density for each material where the substance passes through a quasi-isotropic state and the foam behaves like an isotropic material, where triaxiality phenomena are significant.

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