On some mixed variational principles in magneto-elastostatics

Some mixed variational formulations are presented for the problem of a deforming and magneto-active body completely surrounded by free space. The possibility of large elastic deformations is considered, in particular due to the application of magnetic loads. One-, two- and three-field functionals are studied, for which either the magnetic vector potential or the magnetic field strength serve as leading variable. The relations between the different formulations are explained in terms of Legendre transformations and the Lagrange multiplier method.

► Mixed variational formulations are presented for a deforming, magneto-active body surrounded by free space. ► Large elastic deformations due to the application of magnetic loads are considered. ► One-, two- and three-field functionals are studied. ► Either the magnetic vector potential or the magnetic field strength serve as leading variable. ► The different formulations are related through a Legendre transformations or the Lagrange multiplier method.