A recent theory for stress transmission in isostatic granular and cellular
systems predicts a constitutive equation that couples the stress field to the
local microstructure. The theory could not be applied to macroscopic systems
because the constitutive equation becomes trivial upon straightforward
coarse-graining. This problem is resolved here for arbitrary planar structures.
The solution is based on the observation that staggered order makes it possible
to couple the stress to a reduced geometric tensor that can be coarse-grained.
The method proposed here makes it possible to apply this idea to realistic
systems whose staggered order is generally 'frustrated'. This is achieved by a
renormalization procedure which removes the frustration and enables the use of
the upscalable reduced tensor. As an example we calculate the stress due to a
defect in a periodic solid foam
