A variational principle for magneto-elastic buckling (Q1092700)

The authors postulate explicitely the Lagrangian in terms of the magnetic field in and outside the deformed magnetizable nonconducting body in static situations. A variation of the Lagrangian, under proper constraints, gives the Maxwell-Minkowski equations and boundary conditions. The variational principle yields explicitly the buckling value of the external magnetic field parameter \(B_ 0\) even in the cases where exact solutions for the intermediate (i.e. pre-buckled) and perturbed electromagnetic fields are not available. The authors give the detailed calculations for two cases: for a soft ferromagnetic medium (with a linear relationship between the magnetization and the magnetic field) and for a superconductor (as a non-magnetizable body, for which the current density is concentrated on the surface of the body, and for which the magnetic field inside the body vanishes).