Revisiting the stiffness of lattice plates with micromechanics modeling

Abstract

Plate-like lattice structures have attracted increasing attention due to their excellent structural and functional properties. As the basis of applications, their in-plane and out-of-plane stiffness, especially the mechanism of out-of-plane deformation, still remain insufficiently understood. For a comprehensive understanding of their mechanical behavior, a revisit is made to the in-plane and out-of-plane stiffness of the lattice plates based on theoretical micromechanics modeling and finite element simulations. The deformation mechanism is revealed and analytical expressions of the in-plane and out-of-plane stiffness are derived. It is found that the out-of-plane stiffness is contributed by the torsion and out-of-plane bending deformation of the components. The relation between in-plane and out-of-plane stiffness of the lattice plates is totally different from that of the continuum plate, and is described by a concise formula. The stiffness anisotropy of the lattice structure can be easily on-demand designed using the theoretical model. Furthermore, this theoretical model can also apply to atomic scale 2D nanomaterials when combining with the molecular structural mechanics model. This work gives an insight into the understanding of the mechanical properties of discrete material and would be helpful in the design of lattice materials.