A method for making: (i) a material comprising a network of non-human collagen fibrils, wherein less than 10% by weight of the collagen fibrils in the material are in the form of collagen fibers having a diameter of 5 μm or more, are in the form of fibrils aligned for 100 μm or more of their lengths, or both; wherein said material contains no more than 40% by weight water; and wherein said material contains at least 1% of a lubricant, comprising: fibrillating an aqueous solution or suspension of non-human collagen molecules into collagen fibrils, crosslinking said collagen fibrils by contacting them with at least one crosslinking agent, dehydrating the crosslinked collagen fibrils so that they contain less than 40% by weight water, and incorporating at least 1% by weight of at least one lubricant into said material, prior to, during or after any of said fibrillating, crosslinking and dehydrating; or (ii) a material comprising a network of recombinant non-human collagen fibrils, wherein the collagen contains no hydroxylysine; wherein said material contains no more than 25% by weight water; and wherein said material contains at least 1% of a lubricant comprising: fibrillating an aqueous solution or suspension of recombinant non-human collagen molecules containing no hydroxylysine into collagen fibrils, crosslinking said collagen fibrils by contacting them with at least one crosslinking agent, dehydrating the crosslinked collagen fibrils so that they contain no more than 25% by weight water, and incorporating at least 1% by weight of at least one lubricant into said material, prior to, during or after any of said fibrillating, crosslinking and dehydrating. (i) a material comprising a network of non-human collagen fibrils, wherein less than 10% by weight of the collagen fibrils in the material are in the form of collagen fibers having a diameter of 5 μm or more, are in the form of fibrils aligned for 100 μm or more of their lengths, or both; wherein said material contains no more than 40% by weight water; and wherein said material contains at least 1% of a lubricant, comprising: fibrillating an aqueous solution or suspension of non-human collagen molecules into collagen fibrils, crosslinking said collagen fibrils by contacting them with at least one crosslinking agent, dehydrating the crosslinked collagen fibrils so that they contain less than 40% by weight water, and incorporating at least 1% by weight of at least one lubricant into said material, prior to, during or after any of said fibrillating, crosslinking and dehydrating; or fibrillating an aqueous solution or suspension of non-human collagen molecules into collagen fibrils, crosslinking said collagen fibrils by contacting them with at least one crosslinking agent, dehydrating the crosslinked collagen fibrils so that they contain less than 40% by weight water, and incorporating at least 1% by weight of at least one lubricant into said material, prior to, during or after any of said fibrillating, crosslinking and dehydrating; or (ii) a material comprising a network of recombinant non-human collagen fibrils, wherein the collagen contains no hydroxylysine; wherein said material contains no more than 25% by weight water; and wherein said material contains at least 1% of a lubricant comprising: fibrillating an aqueous solution or suspension of recombinant non-human collagen molecules containing no hydroxylysine into collagen fibrils, crosslinking said collagen fibrils by contacting them with at least one crosslinking agent, dehydrating the crosslinked collagen fibrils so that they contain no more than 25% by weight water, and incorporating at least 1% by weight of at least one lubricant into said material, prior to, during or after any of said fibrillating, crosslinking and dehydrating. fibrillating an aqueous solution or suspension of recombinant non-human collagen molecules containing no hydroxylysine into collagen fibrils, crosslinking said collagen fibrils by contacting them with at least one crosslinking agent, dehydrating the crosslinked collagen fibrils so that they contain no more than 25% by weight water, and incorporating at least 1% by weight of at least one lubricant into said material, prior to, during or after any of said fibrillating, crosslinking and dehydrating.