Existence of Energy Minimizers for Magnetostrictive Materials
Piotr Rybka, Mitchell Luskin · SIAM Journal on Mathematical Analysis · 2005
The existence of a deformation and magnetization minimizing the magnetostrictive free energy is given. Mathematical challenges are presented by a free energy that includes elastic contributions defined in the reference configuration and magnetic contributions defined in the spatial frame. The one-to-one a.e. and orientation-preserving property of the deformation is demonstrated, and the satisfaction of the nonconvex saturation constraint for the magnetization is proven.