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ralfHielscher committed Sep 5, 2023
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Showing 1 changed file with 17 additions and 12 deletions.
29 changes: 17 additions & 12 deletions doc/Plasticity/SingleSlipModel.m
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%%

% We may visualize the orientation depedence of the spin tensor as a quiver
% plot
plot(Omega,'section','sigma')

%%
% or as the divergence of this vectorfield
plotSection(div(Omega),'sigma')
% We may visualize the orientation depedence of the spin tensor by plotting
% its divergence in sigma sections and on top of it the spin tensors as a
% quiver plot

plotSection(div(Omega),'sigma','noGrid')
mtexColorMap blue2red
mtexColorbar

hold on
plot(Omega,'add2all','linewidth',1,'color','k')
hold off

%%
% The divergence plots can be read as follows. Negative (blue) regions
% indicate orientations that increase in volume, whereas positive regions
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% the example example illustrated above with only the second slip system
% beeing active, we would expect the c-axis to align more and more with the
% the z-direction.

%
%% Solutions of the Continuity Equation
% The solutions of the continuity equation can be analytically computed and
% are available via the command <SO3FunSBF.SO3FunSBF.html |SO3FunSBF|>.
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plotSection(odf2,'sigma')

%%
% Lets visualize these solution by their pole figures
% We observe exactly the concentration of the c-axis around z as predicted
% by the model. This can be seen even more clear when looking a the pole
% figures

h = Miller({1,0,0},{0,1,0},{0,0,1},csOli);
plotPDF(odf1,h,'resolution',2*degree,'colorRange','equal')

plotPDF(odf2,h,'resolution',2*degree,'colorRange','equal')
mtexColorbar

%%
% For completeness the pole figures of the other two basis functions.

plotPDF(odf2,h,'resolution',2*degree,'colorRange','equal')
plotPDF(odf1,h,'resolution',2*degree,'colorRange','equal')
mtexColorbar

%%
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%%
% We observe that the pole figure with respect to $n \times b$ is always
% uniform, where $n$ is the slip normal and $b$ is the slip direction.

%
%%
% Since in practice all three slip systems are active we can model the
% resulting ODF as a linear combination of the different basis functions
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