A configuration-enabled multiscale method for porous mechanical metamaterial structures incorporating nonlocal and surface effects

Metamaterials exhibit counterintuitive mechanical behaviors that derive from their artificial mesostructural configuration rather than the mechanical properties of each individual component. However, classical multiscale homogenization methods cannot capture the counterintuitive mechanical behaviors. This paper explores the role of mesoscopic configurations on the counterintuitive mechanical behavior of porous mechanical metamaterial structures, attributing the observed effects to nonlocal and surface effects arising from the configurations. A configuration-enabled multiscale method incorporating nonlocal and surface effects is proposed for porous mechanical metamaterial structures to efficiently and accurately forecast the configuration-induced nonlocal and surface effects. In the mesoscale, a variable-thickness representative volume element (RVE) is constructed; based on the variable-thickness RVE, the intrinsic length parameters of nonlocal and surface effects are calibrated for different configurations, thereby constructing an offline dataset. In the macroscale, porous mechanical metamaterial structures are modeled as homogenization structures incorporating nonlocal and surface effects, and the closed-form solution of displacements is derived for porous mechanical metamaterial bars. With the help of the offline dataset of the intrinsic length parameters and the closed-form solution of displacements, the performance of the proposed configuration-enabled multiscale approach, evaluated in terms of accuracy and computational efficiency, is directly compared to a high-fidelity finite element method (FEM) that fully solves the mesoscopic structural configuration. Results indicate that the configuration-enabled multiscale method incorporating nonlocal and surface effects not only offers an accurate representation of the multiscale architecture, significantly outperforming the classical multiscale homogenization approach, but also significantly reduces the computational efficiency of the high-fidelity FEM.