PSI - Issue 40

L.R. Akhmetshin et al. / Procedia Structural Integrity 40 (2022) 7–11 L.R. Akhmetshin / Structural Integrity Procedia 00 (2022) 000 – 000

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1. Introduction Metamaterials are a class of materials whose effective properties are controlled not only by combining the chemical composition of the base material but also by their structure. Mechanical metamaterials are characterized by unusual mechanical properties. There are also optical, acoustic, and many other metamaterials. A chiral structure is a typical two-dimensional honeycomb structure. Chirality is a property of an object not to overlap with its mirror image. Common chiral honeycombs have three, four, and six bundles attached to them, which can also be divided into chiral and antichiral honeycombs according to the direction of rotation (Fu et al., 1962). Chiral honeycombs are typical structures that have generated much research interest in their constitutive equation (Alderson et al., 2010; Chen et al., 2013), bending analysis (Scarpa et al., 2017), and wave propagation (Tee et al., 2010). Based on the two-dimensional chiral honeycomb, a three-dimensional chiral structure was developed by a spatial combination as reported e.g. in (Frenzel et al., 2017). Three-dimensional (3D) materials are difficult to fabricate, so their research is still insufficient. In recent years, innovations in industrial technology, especially in the development of 3D printing technology, have made mechanical metamaterials a subject of extensive research (Fu et al., 1962). Some metamaterials consisting of chiral structures have a negative or zero Poisson's ratio value (Huang and Chen, 2016; Goldstein et al., 2014). Materials with a negative Poisson's ratio are called auxetics. As a most studied branch of mechanical metamaterials, auxetic materials exhibit counterintuitive deformation behavior under mechanical loading. To be more specific, under uniaxial compression (tension), conventional materials expand (contract) in the directions orthogonal to the applied load. In contrast, auxetic materials contract (expand) in the transverse direction during compression (tension). Accompanied by uncommon deformation pattern under compression and tension, auxetic materials and structures are endowed with many desirable material properties, such as superior shear resistance, indentation resistance, fracture resistance, synclastic behavior, variable permeability, and better energy absorption (Hou et al., 2015; Imbalzano et al., 2017a; Hou et al., 2017; Imbalzano et al., 2017b; Imbalzano et al., 2016; Jiang and Hu, 2017). These aforementioned advantages of auxetic metamaterials make them potential candidates for applications in vehicle construction, bioengineering, and many other fields (Bhullar et al., 2015). Some design features of tetrachiral structures were described in (Akhmetshin and Smolin, 2020). A review of the literature on auxetics showed that studies of the effective Poisson's ratio are mainly conducted on two-dimensional metamaterials. Determining the effective Poisson's ratio for three-dimensional chiral structures is not an easy task because of their unconventional behavior. Solving this problem is a necessary addition to the study of mechanical metamaterials. For minor deformations, some authors use micropolar material models (Sadovskii, 2020). The purpose of this work is to investigate the effective Poisson's ratio of a mechanical metamaterial sample consisting of cellular tetrachiral structures. The effective Poisson's ratio of this structure is analyzed in the framework of linear elasticity theory. 2. Numerical modeling Consider the creation of a three-dimensional rod from a mechanical tetrachiral metamaterial (Fig. 1). A sample in the form of a rod consists of 81 unit cells, 9 cells along Y-axis and 3 cells along X and Z axes. Each face of the unit cell has a tetrachiral structure (Fig. 1a). Elementary cell of the metamaterial has the shape of a hollow cube (Fig. 1b). In this paper, chirality is represented in the connection of the ring and ligaments (ribs) connected to the ring tangentially. Prefix ‘tetra’ in the name means in the name denotes the four bundles in the structure. T he geometric model was created in the «Design Modeler» module of the Ansys Workbench software package.