An FEM-based homogenization method for orthogonal lattice metamaterials within micropolar elasticity

Abstract

Lattice metamaterials are widely used in weight-critical applications and gain more design freedoms with the development of additive manufacturing technology, which requires new accurate homogenization methods to model the mechanical behavior of complex microstructures. In the present work, a new homogenization method based on finite element methods was proposed within the frame of the anisotropic micropolar continuum for the metamaterial, which provided a general approach for both homogeneous and conformal metamaterials of orthogonal lattices. The mapping relation between lattice and finite element mesh as well as edge effects were clarified and modeled. The homogenization approach is verified based on detailed modal analysis and shows high numerical accuracy for engineering applications. Computational experiments confirmed that the micropolar model provides much more accurate results than the classical continuum.