Biocompatible polyurethanes with thermally-induced shape memory properties derived from three-arm branched poly(ε-caprolactone-co-γ-butyrolactone)-b-poly(lactide) block copolymers

•A biocompatible and thermally-induced shape memory poly(lactide)-based polyurethane with a cross-linked network structure was synthesized through the chain extension of three-arm branched poly(ɛ-caprolactone-co-γ-butyrolactone)-b-poly(lactide) block copolymers with HDI.•The enhanced molecular weight of PLA blocks restricted the crystallization of flexible PCBL blocks. Concurrently, stereocomplexation accelerated the crystallization of the PLA blocks.•The mechanical property, shape memory performance, thermal stability and hydration ability of the poly(lactide)-based polyurethane could be significantly adjusted by the molecular weight, optical activity and stereocomplexation of PLA block.•The synthesized polyurethanes were assessed for biocompatibility through in vitro hemolysis, cytotoxicity, and live/dead staining tests, demonstrating their excellent compatibility.