A finite strain continuum theory is advanced for static and dynamic simulations of material
response under combined mechanical and magnetic fields. The general thermomechanical
theory accounts for nonlinear thermoelasticity, plastic flow from slip and twinning, damage
mechanics from voids, and phase transformations. Maxwell’s equations are implemented in the Galilean approximation. Effects of electromechanical body forces, Maxwell’s stress, and magnetostriction are included, as are forces and heating from electric currents in conductors. Several assumptions are introduced to facilitate calculations in the context of finite element methods with explicit dynamics. These include assumptions of small deviatoric elastic strains, an additive decomposition of the spatial deformation rate tensor, and a composite flow rule for mechanisms of slip, twinning, and deviatoric deformation of phase transformations whose individual contributions cannot be discerned from experimental data. Of particular interest are ferrous solids whose phase changes and interactions are affected by external magnetic fields. Predictions for compression of pure iron, in comparison with experimental data and prior analytical results, verify suitability of modeling assumptions. Further calculations demonstrate efficacy of the model for reproducing experimental findings on ferrous alloys of the same chemical composition but with two different prior heat treatments, leading to different initial microstructures. These alloys are deformed quasi-statically, in tension, with and without transverse fields. Effects of magnetic field on kinetic barriers are discovered to be more influential on phase transitions than magnetic Gibbs free energy differences between phases.