PSI - Issue 5

Danuta Miedzińska et al. / Procedia Structural Integrity 5 (2017) 484– 491 Danuta Miedzińska / Structural Integrity Procedia 00 (2017) 000 – 000

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older RAND functions the cycle of repeating numbers was too short. Finally, RAND() returns an evenly distributed random real number greater than or equal to 0 and less than 1. A new random real number is returned every time the worksheet is calculated. 4. Numerical models and analyses The selection of homogenization method was based on the literature review. The most important are methods presented by Vemaganti and Deshmukh (2006), Sills at al. (2002) and Dong (1983), where the functionally graded material homogenization was proposed. The general method of FGM homogenization was shown in Figure 4. The method is based on a division of microstructure into relevant elements (here strips), for which the substitute properties are calculated. The selection of a strip width to achieve the smallest error of homogenization is carried out on the base of local microstructure observation and the calculations for series of models with different strips width.

Fig. 4. Scheme of applied homogenization method by Vemaganti and Deshmukh (2006).

For the test of the homogenization method presented above the selected model of functionally graded material with linear change in porosity on the sample height was used – Figure 5. In the next stem the FGM model with normal distribution change in porosity on the sample height was tested – Figure 6.

Fig. 5. Model of FGM with linear change in porosity on the sample height.

Fig. 6. Model of FGM with normal distribution(mean 50, standard deviation 30) change in porosity on the sample height.

The uniaxial compression test was carried out with the use of LS Dyna computer code. The boundary conditions and base material model were similar to those applied for RVE calculations (see Section 2).