Analysis of some methods of integration of cells in a mechanical metamaterial

In this paper, the influence of integration of unit cells on the mechanical behavior of the sample made of mechanical tetrachiral metamaterial is studied by using mathematical modeling. A chiral structure of the cells provides unusual mechanical behavior of the metamaterial, namely, twisting under uniaxial loading. Two methods of integration of unit cells in the metamaterial are discussed: joining and overlapping. The advantages and disadvantages of each method are described. It has been found that in one of the cases, the rotation of the system of two cells is carried out around the center of mass, which favorably affects the stability of the system, but decreases the rotation angle. In another case, the absence of one of the faces leads to the rotation which is not relative to the center of mass and results in the asymmetric strain figure and instability of the system. Such instability is caused by disproportionate arrangement of the cells in the plane, which has been shown using the examples of the systems with two and nine cells. For the system of nine unit cells, both methods of integration lead to a symmetric rotation about two perpendicular axes. Further research of this topic is supposed to allow one to create metamaterials and structures with programmable mechanical behavior.