On an analogy between plane finite elastic deformations and certain magnetohydrodynamic flows (Q1058886)

In this paper the authors give an analogy between plane strain finite elastic deformations of an incompressible neo-Hookean or Mooney material and certain steady magnetohydrodynamic flows. They obtain (although the analogy does not provide a precise formal mathematical equivalence) various results (semi-inverse techniques, solution types) which are applicable in other areas. Obtained are a restricted form of Adkins' reciprocal theorem (for magnetohydrodynamic systems) and two new classes of exact solutions for magnetohydrodynamic systems which are motivated by well-known deformations in finite elasticity.