  Isostaticity theory (IT) provides stress field equations for marginally rigid
packs of non-cohesive particles, interacting through hard-core forces. Its main
advantage over strain-based theories is by closing the stress equations with
stress-structure, rather than stress-strain, relations, which enables modelling
the stress chains, often observed in experiments and simulations. The
usefulness of IT has been argued to extend beyond its applicability at marginal
rigidity. It has been shown to be derivable from first principles in
two-dimensions, with the structure quantified by a fabric tensor that couples
to the stress field. However, upscaling IT to the continuum is done currently
empirically by postulating convenient closure equations. The problem is that a
volume average of the fabric tensor vanishes in the continuum limit,
trivialising the closure equation. This poses an unusual upscaling problem,
necessitating a new approach. Such an approach is developed here, resolving the
problem for planar granular assemblies. The new method is developed initially
for idealised 'unfrustrated' packs by coarse-graining first to the two-grain
scale, after which a conventional coarse-graining can be used. It is then
extended to general realistic systems, by introducing an intermediate
`de-frustration' procedure. The applicability of the method is illustrated with
a tractable example.

Soft Condensed Matter;Classical Physics