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Table 3 Relative displacement, accumulated plastic strain and stress deviations of the multiscale problem with a elastoplastic RVE for different numbers of POD modes at time point of maximum loading

From: Displacement-based multiscale modeling of fiber-reinforced composites by means of proper orthogonal decomposition

 

\(u_x\)

\(u_y\)

\(u_z\)

\(\varepsilon _{pl}\)

  

\(m=6\)

\(2.8\cdot 10^{-3}\)

\(5.5\cdot 10^{-4}\)

16.5

\(4.8\cdot 10^{-3}\)

  

\(m=12\)

\(5.0\cdot 10^{-4}\)

\(1.6\cdot 10^{-4}\)

4.5

\(7.0\cdot 10^{-4}\)

  

\(m=24\)

\(1.5\cdot 10^{-4}\)

\(4.5\cdot 10^{-5}\)

0.7

\(1.5\cdot 10^{-5}\)

  
 

\(\sigma _{xx}\)

\(\sigma _{yy}\)

\(\sigma _{zz}\)

\(\sigma _{xy}\)

\(\sigma _{xz}\)

\(\sigma _{yz}\)

\(m=6\)

\(1.3\cdot 10^{-2}\)

\(2.5\cdot 10^{-3}\)

\(4.3\cdot 10^{-3}\)

\(1.1\cdot 10^{-2}\)

12.8

1.0

\(m=12\)

\(1.9\cdot 10^{-3}\)

\(7.4\cdot 10^{-4}\)

\(9.5\cdot 10^{-4}\)

\(2.4\cdot 10^{-3}\)

2.3

0.4

\(m=24\)

\(6.6\cdot 10^{-5}\)

\(2.9\cdot 10^{-4}\)

\(5.3\cdot 10^{-5}\)

\(2.2\cdot 10^{-4}\)

0.15

0.19

  1. The table gives the maximum values of the relative deviation \(|\Delta (*)|^*=|\overline{(*)} - (*)|/max(|(*)|)\) of each field \(\overline{(*)}\) computed in the FEPOD computation in comparison with the corresponding field \((*)\) of the reference FE\(^2\) computation for the multiscale example with elastoplastic material behavior and a different number of POD modes