Currently, mesenchymal stem cells (MSCs)‐based therapies for bone regeneration and treatments have gained significant attention in clinical research. Though many chemical and physical cues which influence the osteogenic differentiation of MSCs have been explored, scaffolds combining the benefits of Zn²⁺ ions and unique nanostructures may become an ideal interface to enhance osteogenic and anti‐infective capabilities simultaneously. In this work, motivated by the enormous advantages of Zn‐based metal–organic framework‐derived nanocarbons, C‐ZnO nanocarbons‐modified fibrous scaffolds for stem cell‐based osteogenic differentiation are constructed. The modified scaffolds show enhanced expression of alkaline phosphatase, bone sialoprotein, vinculin, and a larger cell spreading area. Meanwhile, the caging of ZnO nanoparticles can allow the slow release of Zn²⁺ ions, which not only activate various signaling pathways to guide osteogenic differentiation but also prevent the potential bacterial infection of implantable scaffolds. Overall, this study may provide new insight for designing stem cell‐based nanostructured fibrous scaffolds with simultaneously enhanced osteogenic and anti‐infective capabilities.

In this paper, size effects exhibited by mechanical metamaterials have been studied. When the sizescale of the metamaterials is reduced, stiffening or softening responses are observed in experiments. In order to capture both the stiffening and softening size effects fully, a second-order asymptotic homogenization method based on strain gradient theory is used. By this method, the metamaterials are homogenized and become effective strain gradient continua. The effective metamaterial parameters including the classical and strain gradient stiffness tensors are calculated. Comparisons between a detailed finite element analysis and the effective strain gradient continua model have been made for metamaterials under different boundary conditions, different aspect ratios, different unit cells (closed or open cells) and different topologies. It shows that both stiffening and softening size effects can be captured by using the effective strain gradient continua models.

In this paper, a strain gradient continuum model for a metamaterial with a periodic lattice substructure is considered. A second gradient constitutive law is postulated at the macroscopic level. The effective classical and strain gradient stiffness tensors are obtained based on asymptotic homogenization techniques using the equivalence of energy at the macro- and microscales within a so-called representative volume element. Numerical studies by means of finite element analysis were performed to investigate the effects of changing volume ratio and characteristic length for a single unit cell of the metamaterial as well as changing properties of the underlying material. It is also shown that the size effects occurring in a cantilever beam made of a periodic metamaterial can be captured with appropriate accuracy by using the identified effective stiffness tensors.