Magnetic materials and methods exhibit large magnetic-field-induced deformation/strain (MFIS) through the magnetic-field-induced motion of crystallographic interfaces. The preferred materials are porous, polycrystalline composite structures of nodes connected by struts wherein the struts may be monocrystalline or polycrystalline. The materials are preferably made from magnetic shape memory alloy, including polycrystalline Ni—Mn—Ga, formed into an open-pore foam, for example, by space-holder technique. Removal of constraints that interfere with MFIS has been accomplished by introducing pores with sizes similar to grains, resulting in MFIS values of 0.12% in polycrystalline Ni—Mn—Ga foams, close to the best commercial magnetostrictive materials. Further removal of constraints has been accomplished by introducing pores smaller than the grain size, dramatically increasing MFIS to 2.0-8.7%. These strains, which remain stable over >200,000 cycles, are much larger than those of any polycrystalline, active material.