# PSI - Issue 56

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Author name / Structural Integrity Procedia 00 (2019) 000–000

Kevin Moj et al. / Procedia Structural Integrity 56 (2024) 120–130

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Table 3. Overview of results from dimensional deviation and porosity analysis. No. Porosity (%) Average defect volume (mm 3 ) Average dimensional deviation (mm) Real relative density (%) 1 0.096 0.00012 0.032 28.17 2 0.0332 0.00009 0.0092 48.78 3 0.04 0.00065 0.0035 24.58 4 0.01 0.00025 0.0037 47.82 5 0.17 0.00006 0.028 27.59 6 0.12 0.000067 0.024 50.28 7 0.1 0.000083 0.0037 24.97 8 0.06 0.00012 0.003 48.04 9 0.22 0.000065 0.033 29.73 10 0.13 0.000093 0.016 50.59 11 0.05 0.00015 0.018 26.96 12 0.05 0.00014 0.0016 49.33 13 0.05 0.000076 0.021 27.1 14 0.17 0.000049 0.01012 48.31 15 0.04 0.0001 0.0093 24.31 16 0.05 0.00013 0.00041 48.03 3.3. Numerical homogenization of cellular structures Numerical homogenization consists in determining the effective elastic parameters based on knowledge of the properties of a representative volume. In the case of cellular structures. such a representative volume can be defined as a cell. However. a single cell may be too simplified. Therefore. a simulation was performed using the homogenization method to determine the effect of the number of cells on the resulting mechanical response. The analysis was carried out using a predefined minimum number of cells at which the structure behaves stably. An additional optimization would be a model obtained from a CT scan. which includes information on the actual relative density or porosity. For estimation of the properties of individual cells. a linear model of isotropic elasticity was used. assuming a constant Young's modulus of 163 GPa and a Poisson's ratio of 0.3. Figure 7 depicts the stiffness distribution in red. which indicates the direction of higher stiffness in a cell. while the blue color represents the direction of lower stiffness. For an ideal isotropic material. the stiffness matrix would be represented by a homogeneous sphere. Analysis of the data presented in Table 4 shows that the difference between the distribution of stiffness for one unit cell and the minimum number of cells is not significant. Mostly. the distribution of stiffness for the minimum number of cells is slightly higher. However. in the case of a structure with a Diamond unit cell. the situation changes. This is due to the fact that this topology is not symmetrical. and only using the minimum number of cells will allow to estimate the correct stiffness matrix. It can be seen that there is a close correlation between the actual relative density and the stiffness distribution for models obtained using CT. It is the relative density. rather than the porosity present in the models. that has a greater influence on the formation of cellular properties. Nonetheless. taking all factors into account. in the form of defects or deviations. will allow a more accurate numerical analysis.

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