PARADISCYL:Cylinder-Benchmark

Benchmarks to check PBC in cylinder code

ILL RYU

May 1, 2010

From these benchmarks, we like to confirm if the periodic boundary condition works properly. To do that, two models are prepared. In the first model, square dislocation loop is located at the center of the simulation domain. In the other model, square dislocation loop is split and is put into both top and the bottom surface, as shown in the following figures.

Model geometries

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  [Slip system]

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  [cylinder_square]

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  [cylinder_square_PBC]

To check if PBC works, stresses on the surface are printed out in each cases. After stress components are shifted according to the geometry, values of stress are compared. For simplicity, one vertical line on the cylinder surface is chosen, where stresses are printed out(x and y are fixed). If stress output in both cases are the same, we can conclude PBC works well in the cylinder code.

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Stress calculation in Cylinder code

In cylinder code, stress can be computed by the following equation.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma^{tot}= \sigma^{Inf} + \sigma^{Img}\,\!}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma^{tot}\,\!} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma^{Inf}\,\!} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma^{Img}\,\!} are the total stress, Infinite stress and the image stress. Therefore, each stresses are compared in both models.

Infinite stress

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Image stress stress

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Total stress

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Conclusion

The reason why the infinite stress does not match each other is the infinite stress can have some inaccuracy near the boundary. From the plot, we can conclude that PBC works well in cylinder code, because the stress output fits well to each other. Moreover, we can see zero traction boundary condition is satisfied on the surface of the cylinder.

Input & plot files

ParaDiS input
Matlab file for plot