The invention relates to foamed thermoplastic material articles of manufacture having an internal layered cellular structure (with segmented and varying physical properties across one or more dimensions). In one embodiment, the invention is directed to a multi-layer foamed polymeric article of manufacture having a plurality of discrete physical properties segmented across one or more dimensions, comprising: a non-laminated multi-layer polymeric object having at least one discrete outer layer positioned adjacent to a plurality of discrete inner foamed layers, wherein the at least one discrete outer layer and the plurality of discrete inner foamed layers are integral with one another, and wherein the at least one discrete outer layer has an outer layer physical property and each of the plurality of discrete inner foamed layers has a respective inner foamed layer physical property, wherein the outer layer physical property and the inner foamed layer physical property are different from each other.