Linear vs. Nonlinear Magnetostriction
For the piezomagnetic model, it is possible to express the relation between the stress S, strain ε, magnetic field H, and magnetic flux density B in either a stress–magnetization form or strain–magnetization form. In COMSOL Multiphysics, both constitutive forms can be used; simply select one and the software will make any necessary transformations. You find all the required material data inputs within the Piezomagnetic Material selected in the Solid Mechanics interface.
The nonlinear model of magnetostrictive strain can be used for the whole range from full demagnetization to saturation magnetization. In the case of nonlinear magnetostriction, the magnetization model can be selected. The following options are available: Langevin function, Hyperbolic tangent, User defined, and Linear. The last option will make it possible to find an explicit expression for the magnetization. Note however that such model does not have a proper saturation behavior, and thus it should be used only in the operating range far from saturation. For all other choices, the magnetization vector components will be treated as extra dependent variables.
For more details, see the corresponding theory section in Magnetostriction and Piezomagnetism.