Geometric Design and Inverse Design of Multi-Axial Bistable Lattice Mechanical Metamaterial Inspired by Atomic Arrangement of Crystals

Metamaterials exhibit novel properties which conventional materials do not exhibit. Metamaterials that reversibly transform into two different stable configurations are called bistable metamaterials. Bistable metamaterials are said to absorb kinetic energy with their transformation and are expected to be used as shock-absorbing materials for repeated use. Although many designs of bistable metamaterial have been introduced, most of them exhibit bistability in only one direction and cannot respond to complex stress. In order to create a bistable metamaterial optimal to absorb shock on curved surfaces, it must be possible to respond to multiple directions. In the present research, a novel metamaterial, multi-axis bistable structure (MABS) is introduced. MABS was designed based on atomic arrangement, face-centered cubic (fcc), 3D printed by thermoplastic polyurethane (TPU). Mechanical properties were evaluated by finite element analysis (FEA) and compression tests. The inverse design was introduced to predict design parameters for desired mechanical properties.<br/>To design metamaterial exhibiting bistability in multiple directions, we focused on the symmetry of crystal structures and combined fcc structure with bistable structure. Spheres were placed on atomic positions, and atomic bonds were represented with curved beams. Adjusting design parameters of the spheres and curved beam, mechanical properties of MABS could be optimized. Force—displacement relationship was investigated on 1225 patterns of design parameter with FEA. The relationship between design parameters and mechanical properties was investigated, and inverse design was introduced to optimize the design. MABS was 3D printed with TPU, and compression tests were conducted to evaluate mechanical properties.<br/>MABS can be described by five design parameters. These are the radius of sphere <i>R</i>, the thickness of beam <i>t</i>, the distance between nearest neighboring spheres <i>a</i>, the angle between beam direction and sphere surface <i>φ</i>, the distance between the center of the beam and the center of tetrahedron <i>k</i>. 3D printing some samples of this metamaterial with elastomer and conducting a compression test on the samples, it was found that there some design parameters which MABS becomes bistable, and other design parameters do not make MABS become bistable. FEA simulation was conducted to reveal the criteria to determine whether design parameters make MABS bistable or monostable. As a result, the bistability of MABS depends on the distance between the nearest neighboring spheres <i>a</i> and the distance between the center of the beam and the center of tetrahedron <i>k</i>. MABS becomes bistable when <i>a</i> is smaller, and <i>k</i> is larger. In other words, when the lattice constant of fcc is smaller, and the curved beams are straighter, the second configuration of MABS becomes more stable. The Young’s modulus and critical strength both showed a negative correlation with <i>R</i> and <i>a</i>, a positive correlation with <i>k</i>, and a weak correlation with <i>φ</i>. In advance, inverse design, a machine learning method for inverse problems, was introduced to calculate back the design parameters from desired mechanical properties. This allowed us to design a MABS model with desired mechanical properties.