Mechanical properties of hierarchical lattice via strain gradient homogenization approach

With the advancement of 3D printing technology, manufacturing metamaterials with extreme mechanical properties is becoming more feasible. Hierarchical lattices appear to be ideal candidates for obtaining desirable lightweight, high specific stiffness, and enhanced specific energy absorption. They can be constructed by architected substructures at multiple length scales. The interpretations of the underlying deformation mechanisms are necessary in order to manipulate with expected mechanical properties. In this paper, experiments were conducted to examine the effective mechanical behaviors of hierarchical lattice metamaterials. A strain gradient homogenization approach has been employed to correlate their morphological characteristics to the resulting material properties. The effective stiffness tensors are identified including the fourth-, fifth-, and sixth-order stiffness tensors. The higher-order inertial parameters are determined by a fitting procedure. Comparisons between direct finite element analyses and the homogenized strain gradient continua have been made for hierarchical lattice materials under static and dynamic loads. It is found that strain gradient homogenization approach can be an accurate, efficient and reliable way of predicting the mechanical behaviors of hierarchical lattice. A systematic analysis of geometrical parameters was conducted to uncover the underlying mechanisms responsible for the enhancement of effective properties. This work offers a novel approach for designing the mechanical properties of hierarchical metamaterials through precise control of secondary structure types and distributions.