A method for producing an apertured structured material for accommodating passage of fluids, particularly high viscosity fluids, through the apertured structured material. In one embodiment, the apertured structured material is a composite material formed by differential shrinkage of a shrinkable second layer, for example an ethylene-propylene copolymer, which is laminated to a first layer, for example a polypropylene polymer. During the differential shrinkage process, a plurality of slits which are formed in the second layer open to form uniformly-shaped apertures. In another embodiment, an apertured structured heterogenous material is made of a heterogeneous mixture of at least two homogeneous fiber sets or components having different shrinkage extents.