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Microstructural fields for the 2D elastic microstructure with one circular inclusion. Top row: Fixed sampling pattern with two different numbers of wave vectors. Middle row: Corresponding microstructural stress field σ 11 and reference stress field computed with the full set of frequencies. Bottom row: Absolute difference in the microstructural stress field ∆σ 11 .
Source publication
We present a modified model order reduction (MOR) technique for the FFT-based simulation of composite microstructures. It utilizes the earlier introduced MOR technique (Kochmann et al. [2019]), which is based on solving the Lippmann-Schwinger equation in Fourier space by a reduced set of frequencies. Crucial for the accuracy of this MOR technique i...
Contexts in source publication
Context 1
... that the following observations have been made for all stress and strain fields. The results related to the fixed and adapted sampling pattern are shown in Figure 7 and Figure 8, respectively. In the top row, the sampling patterns for two reduced sets of frequencies (R = 0.78 % and R = 1.54 %) are given. ...
Context 2
... the reduced set of frequencies based on the geometrically adapted sampling pattern and compared to the fixed sampling pattern, a higher amount of low frequencies is needed to capture the microstructural geometry (see Figure 8). Using this reduced set of frequencies also in terms of the microstructure simulation, more accurate results are generated. ...
Context 3
... Figure 12, the geometrically adapted sampling pattern of the microstructure with an annular inclusion is shown. This sampling pattern is similar to the adapted sampling corresponding to the circular inclusion; see Figure 8. Nevertheless, the amount of high frequencies is slightly higher. ...
Context 4
... resulting adapted sampling pattern for R = 1.54 % of frequencies and the corresponding microstructural results are given in Figure 24. Since the 3D case with a spherical inclusion corresponds to the 2D case with a circular inclusion, the resulting sampling patterns are similar, see Figure 8. Also the behavior of the microstructural fields is similar to the 2D case described in Chapter 5.1. ...
Context 5
... that the following observations have been made for all stress and strain fields. The results related to the fixed and adapted sampling pattern are shown in Figure 7 and Figure 8, respectively. In the top row, the sampling patterns for two reduced sets of frequencies (R = 0.78 % and R = 1.54 %) are given. ...
Context 6
... the reduced set of frequencies based on the geometrically adapted sampling pattern and compared to the fixed sampling pattern, a higher amount of low frequencies is needed to capture the microstructural geometry (see Figure 8). Using this reduced set of frequencies also in terms of the microstructure simulation, more accurate results are generated. ...
Context 7
... Figure 12, the geometrically adapted sampling pattern of the microstructure with an annular inclusion is shown. This sampling pattern is similar to the adapted sampling corresponding to the circular inclusion; see Figure 8. Nevertheless, the amount of high frequencies is slightly higher. ...
Context 8
... resulting adapted sampling pattern for R = 1.54 % of frequencies and the corresponding microstructural results are given in Figure 24. Since the 3D case with a spherical inclusion corresponds to the 2D case with a circular inclusion, the resulting sampling patterns are similar, see Figure 8. Also the behavior of the microstructural fields is similar to the 2D case described in Chapter 5.1. ...
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