The presented deformable field theory deals with electromagnetic local forces on the basis of field energy density. In this theory, any movement, rigid or deforming, distorts the electromagnetic field continuum. This leads to novel concepts of total and local forces explicitly related to the elastic deformation gradient rather than the classical gradient of the magnetic field. It is shown how the magnetic vector potential, as the magnetic invariant variable, is associated to this deformable field continuum and is, meanwhile, reference-independent. Then, within an adiabatic virtual work, the local magnetic energy derivatives are analytically performed, converging to overall electromagnetic force and stress tensors, including Lorenz, inherent magnetization and strict magnetostriction forces.