Anisotropic thin foamed polyethylene sheet and applications thereof

A foamed film comprising three co-extruded anisotropic layers including one core foam layer between, and in direct contact with, two solid layers, wherein each of the layers comprises 50 to 100 percent by weight LLDPE with a melt index of 0.2 to 2 g/10 min, and a density in a range of 0.915 to 0.936 g/cm3, and the foamed film has a surface with an average Sheffield smoothness of less than 100, and wherein the core foam layer has a density between 0.56 g/cm3 and 0.935 g/cm3 and a cell density of 102 to 109 cells/cm3 wherein the foamed film has a puncture propagation tear resistance greater than 500 g/mil, and wherein the core foam layer comprises a nucleating agent and has an average cell size of 10 to 100 μm, and wherein a supercritical physical blowing agent is introduced into molten resin inside a mixing section of an extruder, the supercritical blowing agent used is nitrogen, carbon dioxide or a mixture of nitrogen and carbon dioxide.