PARADISCYL:Cylinder-test

Test Cases in cylinder code

ill Ryu and Wei Cai

This tutorial describes test cases to check if cylinder code works well, especially for the image stress calculation. We provide Matlab files which generates ParaDiS inputs and plot the results. The theoretical background is published in Computing Image Stress in an Elastic Cylinder, Journal of the Mechanics and Physics of Solids, 55, 2027 (2007). (PDF) and Dislocation Dynamics Simulations in a Cylinder, Proceedings of the Dislocations 2008 International Conference, IOP Conference Series: Materials Science and Engineering, vol 3,012007 (2009).(PDF)

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TEST1 : Straight edge dislocation along the cylinder axis

In the first test case, image stress of a straight edge dislocation is considered, as shown in the Figure 1, where dislocation is offset(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 \mathbf{x}} ) from the center of the cylinder. We have two cases of 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 \mathbf{x}} =0.5Failed 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 \mathbf{r}} and 0.9Failed 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 \mathbf{r}} .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 \mathbf{r}} is the radius of the cylinder.

(a)	(b)
Fig.1 (a) Isoview (b) Topview.The Bergurs vector is 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 \mathbf{b} = a[1 0 0]} . Since the image stress field of this configuration is solved analytically[Eshelby, J.D., 1979], we compare the image force between the simulation result and analytic solution.The number of grids in circumferential direction is same as the one along the cylinder axis.To consider periodic images along the cylinder axis under PBC, analytical stress field of edge dislocation is implemented in the function of "AllSegmentStress_no_cell_test1" the effect of periodic images along the cylindrical axis (where PBC is applied) is accounted for by including 50 images on each side explicitly, and using a multipole expansion for the rest.