  A new geometrically exact micro-structured model is constructed using a
generalisation of the notion of Riemann-Cartan manifolds and fibre bundle
theory of rank 3. This model is based around the concept of two different
length scales: a macroscopic scale -- of dimensions 1, 2, or 3 -- and a
microscopic one -- of dimension 3. As they interact with each other, they
produce emergent behaviours such as dislocations (torsion) and disclinations
(curvature). A first-order placement map F : TB --> TE between a
micro-structured body B and the micro-structured ambient space E is
constructed, allowing to pull the ambient Riemann-Cartan geometry back onto the
body. I norder to allow for curvature to arise, F is, in general, not required
to be a gradient. Central to this model is the new notion of pseudo-metric,
providing, in addition to a macroscopic metric (the usual Cauchy-Green tensor)
and a microscopic metric, a notion of coupling between the microscopic and
macroscopic realms. A notion of frame indifference is formalised and invariants
are computed. In the case of a micro-linear structure, it is shown that the
data of these invariants is equivalent to the data of the pseudo-metric.
