Shape morphing structures inspired by multi-material topology optimized bi-functional metamaterials

•Shape morphing structures consisted of the bi-functional metamaterial were successfully designed through the parameterization optimization.•Desired morphing behavior were exactly achieved under not only the mechanical loading but rather the thermal and thermomechanical loadings.•Bi-functional metamaterials with the complete geminations of the Poisson’s ratio and coefficient of thermal expansion were obtained through a multi-material topology optimization algorithm.