In continuum physics dislocations are the cause of plastic behaviour of metals. But mathematically they may be thought of as almost two codimensional concentrations of the curl of a matrix field. If the energy of the field is proportional to the square distance to SO(n), then we are able to show a sharp lower energy bound depending on dislocation density in the framework of the geometric rigidity bounds of Friesecke, James, Mueller and others. One (and the main) consequence is that low energy configurations are close to piecewise constant functions with values in SO(n). Most of the results are (ongoing) joint work with Gianluca Lauteri.

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