  Stress transmission in planar open-cell cellular solids is analysed using a
recent theory developed for marginally rigid granular assemblies. This is made
possible by constructing a one-to-one mapping between the two systems. General
trivalent networks are mapped onto assemblies of rough grains, while networks
where Plateau rules are observed, are mapped onto assemblies of smooth grains.
The constitutive part of the stress transmission equations couples the stress
directly to the local rotational disorder of the cellular structure via a new
fabric tensor. An intriguing consequence of the analysis is that the stress
field can be determined in terms of the microstructure alone independent of
stress-strain information. This redefines the problem of structure-property
relationship in these materials and poses questions on the relations between
this formalism and elasticity theory. The deviation of the stress transmission
equations from those of conventional solids has been interpreted in the context
of granular assemblies as a new state of solid matter and the relevance of this
interpretation to the state of matter of cellular solids is discussed.
