Modeling lattice metamaterials with deformable joints as an elastic micropolar continuum

Abstract

Planar lattice metamaterials, such as periodic beam networks, are often considered as the micropolar continuum, where each material point has two translational degrees of freedom and one rotational degree of freedom. The joints through which bars are linked to one another are generally approximated as rigid. This study focuses on lattices with complex-structured deformable joints. The deformation field in each joint is obtained by conducting structural analyses. Once the “stiffness matrix” of the joint-centered unit cell is obtained by the finite element method, it can be used as the input for the standard procedure of calculating micropolar elastic moduli that are based on the equivalence of strain energy. As a result, effective moduli can be expressed in a semi-analytical form, meaning that only the cell structural stiffness is given numerically. The present model is validated by comparison to the FEM simulations. Particularly, the auxetic and anisotropic properties are discussed for various lattice metamaterials with deformable joints. We then take the obtained effective moduli as inputs to the in-house micropolar FEM code and obtain results agreeing well with the FEM structural simulations.