A well-posed and microstructure-emerged homogenization method for nonlocal metamaterial truss

The classical multiscale homogenization methods can only take into account the pure microstructural effect, resulting in the inability to accurately capture the nonlocal interactions emerged from the underlying microstructures of metamaterial structures. This paper explores the nonlocal interplay mechanism that emerged from artificial microstructures and develops a well-posed and microstructure-emerged homogenization method capable of capturing microstructure-emerged nonlocality that is strictly related to its extrinsic and intrinsic length scales. First, we propose a novel nonlocal concentrated element model that accounts for both the pure microstructural effect and the nonlocal interaction mechanism to describe the static response of metamaterial trusses. This model not only considers the pure microstructural effect but also further considers the nonlocal interaction, thus providing a more comprehensive description of the static response of metamaterial trusses. Then, based on the nonlocal concentrated element model, a microstructure-emerged homogenization method is developed for metamaterial trusses with an accuracy comparable to that of high-fidelity numerical methods. Since the developed homogenization method is well-posed, a closed-form solution for the displacement of the metamaterial truss is obtained. High-fidelity finite element simulations show that the effective moduli of different metamaterial trusses have significant nonlocal effects, especially for metamaterial trusses with high porosity. Results indicate that the microstructure-emerged homogenization method provides a robust and accurate representation of the metamaterial truss, significantly outperforming the classical multiscale homogenization methods that only consider pure microstructural effects.