A deep insight into the mechanical properties of Mg-Sc alloys through DFT

•The mechanisms behind the mechanical properties of Mg-Sc-based shape memory alloys have been studied for the first time.•The G-SSNEB was calculated to obtain the energy barrier, and no energy barrier inhibits the MT of 15.625 at.%Sc, 18.75 at.%Sc.•The Fermi surfaces were calculated to prove the bcc structure of 15.625 at.%Sc is difficult to exist.•The contents of Sc undergo reversible martensite transformation is around 18.75 at.%Sc.•The relationship between Sc content, RE (La, Gd, Yb) doping and mechanical properties was revealed, and Gd doping can improve the hardness of Mg-Sc alloy.