A magnetic materials construct and a method to produce the construct are disclosed. The construct exhibits large magnetic-field-induced deformation through the magnetic-field-induced motion of crystallographic interfaces. The construct is a porous, polycrystalline composite structure of nodes connected by struts wherein the struts may be monocrystalline or polycrystalline. If the struts are polycrystalline, they have a "bamboo" microstructure wherein the grain boundaries traverse the entire width of the strut. The material from which the construct is made is preferably a magnetic shape memory alloy, including polycrystalline Ni-Mn-Ga. The construct is preferably an open-pore foam. The foam is preferably produced with a space-holder technique. Space holders may be dissolvable ceramics and salts including NaAlO 2 .