Status and Challenges in Homogenization Methods for Lattice Materials

Lattice structures have shown great potential in that mechanical properties are customizable without changing the material itself. Lattice materials could be light and highly stiff as well. With this flexibility of designing structures without raw material processing, lattice structures have been widely used in various applications such as smart and functional structures in aerospace and computational mechanics. Conventional methodologies for understanding behaviors of lattice materials take numerical approaches such as FEA (finite element analysis) and high-fidelity computational tools including ANSYS and ABAQUS. However, they demand a high computational load in each geometry run. Among many other methodologies, homogenization is another numerical approach but that enables to model behaviors of bulk lattice materials by analyzing either a small portion of them using numerical regression for rapid processing. In this paper, we provide a comprehensive survey of representative homogenization methodologies and their status and challenges in lattice materials with their fundamentals.

Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations

The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.

Stress Wave Propagation and Energy Absorption Properties of Heterogeneous Lattice Materials under Impact Load

A heterogeneous lattice material composed of different cells is proposed to improve the energy absorption capacity. The heterogeneous structure is formed by setting layers of body-centered XY rods (BCCxy) cells as the reinforcement in the body-centered cubic (GBCC) uniform lattice material. The heterogeneous lattice samples are designed and processed by additive manufacturing technology. The stress wave propagation and energy absorption properties of heterogeneous lattice materials under impact load are analyzed by finite element simulation (FES) and Hopkinson pressure bar (SHPB) experiments. The results show that, compared with the GBCC uniform lattice material, the spreading velocity of the stress of the (GBCC)3(BCCxy)2 heterogeneous lattice material is reduced by 18.1%, the impact time is prolonged 27.9%, the stress peak of the transmitted bar is reduced by 34.8%, and the strain energy peak is reduced by 29.7%. It indicates that the heterogeneous lattice materials are able to reduce the spreading velocity of stress and improve the energy absorption capacity. In addition, the number of layers of reinforcement is an important factor affecting the stress wave propagation and energy absorption properties.

How to Surpass the Deep-Sea Glass Sponges Mechanically

The biomimetic design of engineering structures is based on biological structures with excellent mechanical properties, which are the result of billions of years of evolution. However, current biomimetic structures, such as ordered lattice materials, are still inferior to many biological materials in terms of structural complexity and mechanical properties. For example, the structure of \textit{Euplectella aspergillum}, a type of deep-sea glass sponge, is an eye-catching source of inspiration for biomimetic design; however, guided by scientific theory, how to engineer structures surpassing the mechanical properties of \textit{E. aspergillum} remains an unsolved problem. The lattice structure of the skeleton of \textit{E. aspergillum} consists of vertically, horizontally, and diagonally oriented struts, which provide superior strength and flexural resistance compared with the conventional square lattice structure. Herein, the structure of \textit{E. aspergillum} was investigated in detail, and by using the theory of elasticity, a lattice structure inspired by the bionic structure was proposed. The mechanical properties of the sponge-inspired lattice structure surpassed the sponge structure under a variety of loading conditions, and the excellent performance of this configuration was verified experimentally. The proposed lattice structure can greatly improve the mechanical properties of engineering structures, and it improves strength without much redundancy of material. This study achieved the first surpassing of the mechanical properties of an existing sponge-mimicking design. This design can be applied to lattice structures, truss systems, and metamaterial cells.