The present invention relates to a thermoplastic polyurethane obtainable or obtained by reacting a polyisocyanate composition, a chain extender, and a polyol composition, wherein the polyol composition comprises at least one polyol (P1) which has a molecular weight Mw in the range from 500 to 2500 g/mol and has at least one aromatic polyester block (B1), wherein the polyol (P1) includes 20% to 70% by weight of the aromatic polyester blocks (B1), based on the overall polyester polyol (P1). The present invention further relates to a process for producing a shaped body comprising such a thermoplastic polyurethane, and to shaped bodies obtainable or obtained by a process of the invention.