The kinematics of a micro-structured material is geometrically modelled through the framework of fibre bundle geometry. The material continuum is a fibre bundle B over BB, thought of as the disjoint union of microscopic spaces within each X in BB, where BB is a compact and orientable macroscopic space. It is commonly agreed that connections with curvature and torsion can describe defect densities in micro-structured materials. The aim of this work is to introduce a method to derive these objects from the kinematics in an intrinsic way and derive the generic form of a frame invariant energy in such a model. The material bundle B is therefore placed in the Euclidean fibre bundle E=T(EE) over EE using a punctual placement map phi: B -> E. A first-order placement map Fb: TB -> TE generalizing Tphi is then introduced. This placement has a macroscopic, a microscopic and a mixed part as in Eringen's work. A macroscopic metric on EE, a connection on E and a solder form on E are canonically prescribed from the Euclidean structure on E. Using those, a generalisation of the notion of metric is prescribed on E. This later takes the form of a pseudo-metric, defined as the only one satisfying a certain compatibility condition with the connection, solder form and macroscopic metric. Finally, using F, a metric on BB, a connection on B, a solder form on B and a pseudo-metric on B are inferred. A generalisation of the Galilean group is proposed, and the orbit of all possible first-order placement maps F under this group are computed. Invariance of the energy under this group, analogous to the notion of frame indifference, is then shown to be equivalent to the expressibility of the energy as a functional of the induced macroscopic metric on BB and pseudo-metric on B. Furthermore, it is proven that the data of those two objects is equivalent to the data of the induced material connection, material solder form and a notion of material microscopic metric, canonically obtained from the material pseudo-metric. Finally, it is shown how the proposed model includes some well known models such as Eringen microcontinua, Cosserat media and Timoschenko or Euler-Bernoulli beams.