PSI - Issue 40

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L.R. Akhmetshin et al. / Procedia Structural Integrity 40 (2022) 7–11 L.R. Akhmetshin / Struc ural Integrity Procedia 00 (2022) 0 0 – 0 0

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a

b

c

Fig. 1. Construction of the metamaterial: (a) two-dimensional structure, (b) unit cell of the metamaterial, (c) the sample of the metamaterial.

The parameters determining the geometric dimensions of the unit cell are as follows: L = 50 mm is the length of the unit cell, t = 5 mm is the width of the rib, h = 5mm is the thickness of the rib, r 2 = 17.5mm is the outer radius of the ring element, r 1 = 12.5 mm is the inner radius of the ring element, θ is the slope angle of the ligament. The angle θ is plotted between the metamaterial ligament and the horizontal plane and is dependent on the parameters R = ( r 1 + r 2 ) /2 and l , calculated as:

   .

   2 2 arccos R

(1)

 

L

The problem of uniaxial loading of the mechanical metamaterial sample was solved in the framework of linear elasticity theory. Isotropic Hooke's law was chosen as the constitutive relation. The elastic constants used in this work are taken as, E = 2.6 GPa is Young's modulus, ν = 0.4 is Poisson's ratio. The constants corresponds to the ABS plastic material. Numerical modeling was performed using the finite element method in the ANSYS software package. The unit cell is treated as the system of beams which are modeled as a set of three-dimensional solid elements in the finite element calculations. The uniaxial loading was simulated using the following boundary conditions. At the bottom, the displacement and rotation constraints are set. To the upper face, the displacement along the axis of the rod is set. The displacement corresponds to uniaxial compression of the sample by 15 mm or 3.6 % of compressive strain. 3. Results and discussion Under uniaxial loading of the square cross-section rod, the tetrachiral structure begins to rotate relative to the ring and the sample is twisted. This phenomenon is found in structures with the tension-torsion coupling effect. In this case, the deformation of one edge of the rod occurs in several planes. This is the main problem in determining the effective Poisson's ratio in a rod with this type of deformation. Homogenization methods to determine the effective Poisson's ratio in a tetrachiral structure are not applicable because there is no periodicity of unit cells. Therefore, it is necessary to investigate each edge of the sample ( XY and ZY planes). For observation, 80 fixed points located on the ribs evenly along the length of the sample were selected. Figure 2 shows the value of deviations of the fixed points from their initial positions. When looking at the four