is appropriate for an individual with high density hair growth the stabilizing rings 16 on each hairpiece 10 are substantially concentric the stabilizing rings 16 add structural integrity to the hairpiece 10 the nylon monofilament used in the present invention does not stretch noticeably under the forces typically applied by individuals during daily application and removal of the present hairpiece 10 that is the tensile strengths of the first set of fibers 18 the second set of fibers 20 and the stabilizing rings 16 are higher than the forces applied during normal use of the hairpiece 10 however the hairpiece 12 will easily deform under forces of typical magnitude which are applied in a direction that is not coaxial with the nylon monofilament since the stabilizing rings 16 are not co axial with either the first or second set 18 20 of fibers the presence of the rings 16 substantially increases the likelihood that forces applied to the substrate 12 will be directed along a nylon filament this increased likelihood results in a concomitant increase in structural rigidity throughout the hairpiece 10 in keeping with the objects of the present invention the stabilizing rings 16 advantageously continue to reinforce the substrate 12 even after the hairpiece 10 has been customized to follow the contours of an individual 39 s head the stabilizing rings 16 have a tensile strength which is lower than the tensile strength of the first.