PSI - Issue 56

Kevin Moj et al. / Procedia Structural Integrity 56 (2024) 120–130 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3. Results 3.1. Effect of the unit cell number on the mechanical properties of the structures

The findings indicate that the effective Young's modulus of the cell structure increases with the number of cells. However. the growth rate decreases as the number of cells increases and reaches a plateau at some point. Depending on the two key parameters of the structure. the relative density and the topology of a single cell. each structure has a different stability. To better interpret this phenomenon. an algorithm was developed (Fig.4). Based on such methodology. a numerical analysis was carried out for different single cell shapes and relative densities. Based on preliminary results. the effect of single cell size was found to be negligible. The whole algorithm was divided into two stages. The first criterion refers to the dependence of the change in effective Young's modulus on the number of cells ∆ ��� ��� � . Based on this function. a power approximation was estimated. If the correlation coefficient is greater than or equal to 0.85. the criterion of the power approximation of the relationship ∆ ��� ��� � . was applied. If the correlation coefficient is less than 0.85. a criterion based on the logarithmic approximation of the dependence of the effective Young's modulus on the number of cells ��� ��� � was used. More significance was assigned to the

Fig. 4. Algorithm for determining the number of minimum single cells. power approximation due to the fact that this function is characterized by the presence of a horizontal asymptote. In addition. a stability parameter of �� 0.85 was introduced into the equations. which are presented in Figure 4. Based on the algorithm. the minimum number of cells for a given unit cell and relative density were defined. The results for each set of parameters are shown in Table 2.