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 a polyol (P1) which has a molecular weight Mw in the range from 1500 to 2500 g/mol and has at least one aromatic polyester block (B1). 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.