  The fully nonlinear (geometric and material) system of Field Dislocation
Mechanics is reviewed to establish an exact analogy with the equations of ideal
magnetohydrodynamics (ideal MHD) under suitable physically simplifying
circumstances. Weak solutions with various conservation properties have been
established for ideal MHD recently by Faraco, Lindberg, and Szekelyhidi using
the techniques of compensated compactness of Tartar and Murat and convex
integration; by the established analogy, these results would seem to be
transferable to the idealization of Field Dislocation Mechanics considered. A
dual variational principle is designed and discussed for this system of PDE,
with the technique transferable to the study of MHD as well.
