PARADISCYL:Cylinder-Benchmark2

Benchmarks to check traction boundary condition on the surface

ILL RYU

May 1, 2010

From these benchmarks, we like to confirm if the zero traction boundary condition is satisfird on the surface, which means that the traction force should be zero on the cylinder boundary. To do that, two models are prepared , varying the geometry of dislocation loop, as following figures.

Model geometries

• 

  [flat loop]

• 

  [Inclined loop ]

To satisfy traction zero boundary, we need to check if $\sigma _{rr}\,\!$ ,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_{r \theta}\,\!} , 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_{rz}\,\!} can be zero on the surface.

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Total stress on the cylinder surface

• 

  [flat loop]

• 

  [Inclined loop ]

Conclusion

Based on the plot, we can see that 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_{rr}\,\!} ,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_{r \theta}\,\!} , 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_{rz}\,\!} are zero on the surface.Therefore, the traction boundary condition is satisfied well.

Input & plot files

ParaDiS input
Matlab file for plot