Dislocations are defects in the spatial structure of crystals. Using the framework of differential geometry dislocations are commonly modeled by the torsion tensor. Such a description is limited to crystalline materials.

Here we suggest that dislocations can be described by a torsion-free field – the reference metric. This tensorial field expresses the local equilibrium (stress free) geometry within the material. In this Riemannian description, dislocations are geometric “charges” of intrinsic reference curvature. The model is not based on the crystalline structure of the material. Therefore, it can describe dislocations even in amorphous materials.

We provide explicit expression for the well known Edge dislocation, which is a dipole of curvature. We continue by deriving expressions to a hierarchy of curvature multipoles and show the complete analogy to 2D electrostatics.