The invention is directed at a method for welding a composite material and to welded structures thus prepared. The method includes a step of contacting a substrate material with a composite material, wherein the composite material includes a pair of spaced apart steel sheets and a core layer between the sheets; the volume of the core layer is about 25 volume % or more, based on the total volume of the composite material; the core layer includes a plurality of steel fibers arranged in one or more masses of fibers that extend the thickness of the core layer so that the core layer is in electrical communication with the steel sheets; and the steel fibers have a cross sectional area perpendicular to the length of the fibers from about 1×10−5 mm2 to about 2.5×10−2 mm2.