Disposable absorbent articles having a topsheet; a backsheet having an elastic layer and a constricting layer; and an absorbent core structure having an open-celled absorbent foam material disposed between the topsheet and the backsheet. The absorbent foam material includes a plurality of discrete foam pieces, wherein the discrete foam pieces are separated from neighboring pieces by a Relaxed Gap of from about 10 microns to about 280 microns, as measured according to the SEM Imaging Method. The articles exhibit an OD Full Product Force Threshold at 15 mm extension of greater than 7.2 N, as measured according to the Simple Tensile Method.