An apparatus for manufacturing an elastic composite structure for an absorbent sanitary product includes an anvil with weld pattern comprising at least one anchoring region and at least one deactivating region. The anchoring region includes anchoring welds that form anchoring bonds that fuse facing web layers and anchor elastic thread(s) in position relative to the facing web layers. The deactivating region includes a break bar constructed to sever the thread(s). A method of manufacturing the elastic composite structure includes positioning a tensioned elastic thread between web layers, fusing the web layers to form an anchored zone that includes anchoring bonds that fuse the web layers and anchor the tensioned elastic thread therebetween, and cutting the thread to form a deactivated zone between adjacent portions of the anchored zone that is free of tensioned threads. The method further includes fusing the web layers within the deactivated zone.