Influence of Topological Defects on the Mechanical Response of Unit Cells of the Tetrachiral Mechanical Metamaterial

Abstract

The primary benefit of metamaterials is that their physical and mechanical properties can be controlled by changing the structure geometry. Numerical analysis tools used in this work offer a few advantages over full-scale testing, consisting of an automated process, as well as lower material and time costs. The investigation is concerned with the behavior of unit cells of the tetrachiral mechanical metamaterial under uniaxial compression. The base material is studied within an elastic mathematical model. The influence of topological defects of the unit cell on the metamaterial properties is studied for the first time. Defects, and especially topological defects, play a decisive role in the mechanical behavior of materials and structures. The unit cell without defects reveals orthotropy of properties. Torsion of a cell with a chiral structure is induced by the rotation of all tetrachiral walls, and therefore it is sensitive to the introduction of defects. There are cases of increased torsion as well as of no compression–torsion coupling effect. In the latter case, the unit cell experiences only shear. The effective Young’s modulus is calculated to vary in the range from 23 to 57 MPa for unit cells of different topologies. With the successive introduction of defects in two walls, the studied characteristics increase, correlating with each other. A further increase in the number of defects affects the characteristics in different ways. The introduction of two more defects in the walls decreases torsion and increases Young’s modulus, after which both characteristics decrease. The introduction of topological defects in all walls of the unit cell leads to the orthotropic behavior of the cell with the opposite sign of torsion.