Response Evolution of a Tetrachiral Metamaterial Unit Cell under Architectural Transformations

This paper studies a mechanical metamaterial with tetrachiral topology by mathematical modeling. Chirality is the property of an object that makes the object distinguishable from its mirror image; chirality can be left- or right-handed. The mechanical response of two metamaterial unit cells with different configurations (patterns A and B) is investigated. It is found that the cubic cell with a regular pattern A exhibits orthotropic mechanical behavior under loading along three coordinate axes. An irregular pattern B differs from pattern A in that the upper face of the unit cell has an opposite chirality. This architectural transformation is considered as a topological defect, which enhances the twisting effect in the loaded metamaterial. Analysis of displacements and stresses shows that the mechanical behavior of the pattern B cell is described by the model of a transversely isotropic material. The orthotropic and transversely isotropic behavior of the cells of given configurations is also confirmed by the values of the effective elastic constants. Microstructural geometry and mechanical deformation of metamaterials are shown to be closely related. It is shown that a topological defect in a unit cell of a tetrachiral metamaterial strongly determines its twisting behavior.