Nonwoven materials having discrete three-dimensional deformations therein forming protrusions that extend outward from the first surface of the nonwoven material and wide base openings adjacent to the second surface of the nonwoven material are disclosed. The nonwoven materials include multiple fibers that extend from the base of the protrusions to the distal end of the protrusions, and contribute to form a portion of the sides and cap of a protrusion. Such fibers may at least substantially surround the sides of the protrusions.