Effective Poisson’s ratio of tetrachiral mechanical metamaterial

Abstract

The problem of computational determination of the effective Poisson’s ratio for a mechanical metamaterial having a tetrachiral structure is considered. The problem is solved numerically in the three-dimensional formulation based on the finite element method. The problem is that during uniaxial loading of the sample made of the considered metamaterial it is twisted. This makes it difficult to determine the transverse strain. For observation, 80 fixed points located on the ribs evenly along the length of the sample were selected. When looking at the four equidistant fixed points, it can be found that the deviations in the X-axis and Z-axes are commensurate. This indicates that the distance between the points on the straight line perpendicular to the axis of loading does not change, so there is no transverse deformation. From this, it was concluded that the value of the effective Poisson’s ratio is zero. The zero value can be explained by the fact that there are transverse elements in the structure. During longitudinal compression, the transverse edges do not twist, which could lead to a contraction in the cross-section of the rod.