The following post breaks down and explains the postprocessing and
visualization steps used to create the images and video for the
axisymmetric stress-strain brake disk analysis model. By using the Octave or MATLAB command line and exported
finite element *fea* data struct one can create custom graphics and
visualizations that is currently not possible to do within the FEATool
graphical user interface (GUI).

The first step in creating the advanced visualizations is to run the
FEATool model example m-script file to generate and return the finite
element analysis struct *fea*, together with the solution stored in
the *fea.sol.u* field (in this case the automatic pre-defined plots
can be turned off with the `‘iplot’, ‘0’`

flag, since
postprocessing will be done manually)

```
fea = ex_axistressstrain4( 'iplot', 0 );
```

Next, model constants and parameters used in during postprocessing are prescribed

```
deltad = 5.5e-3; % Disk thickness.
rd = 66e-3; % Disk inner radius.
rp = 75.5e-3; % Pad inner radius.
Rd = 113.5e-3; % Disk outer radius.
```

Continuing, the solution vector for all time steps is saved in a
temporary variable *u* (the solution at each time step corresponds to
a column in *u*). The parameters *cmax* and *cmin* are also calculated
which later are used to fix the colormap range (otherwise not much
difference between hot and cold maxima can be seen)

```
u = fea.sol.u;
cmax = max(u(:)) - 273.15;
cmin = 0;
```

Coordinates to plot and visualize the contours and boundaries of the
brake disk must also be defined (here the assumption is that the disk
is centered at the origin with the radial coordinate spanning the
*x-z* plane)

```
% Points around the circumference.
npth = 72;
th = linspace( 0, 2*pi, npth );
% Inner coordinates.
x = rd*cos(th);
z = rd*sin(th);
% Outer coordinates.
xx = Rd*cos(th);
zz = Rd*sin(th);
y = deltad*ones(size(x));
```

The `ringgrid`

function is also
used to generate coordinates around the disk in the grid struct
variable *g* and evaluation points in *rz*. These will be used to
interpolate the temperature field from axisymmetric coordinates to
three dimensions (the ring grid can be seen and visualized by itself
using the `plotgrid( g )`

command)

```
npr = 25;
g = ringgrid( npr-1, npth-1, rd, Rd );
r = sqrt( g.p(1,:).^2 + g.p(2,:).^2 );
rz = [rd+sqrt(eps) rd+(Rd-rd)/2 Rd-sqrt(eps);deltad/2*[1 1 1]];
```

Now, the actual plotting is initialized by creating a figure window to draw in, an empty array for the stresses at the three points (inner radius, outer radius, and the mid point), and starting the postprocessing loop

```
figure
st = zeros(3,1);
for i=1:size(u,2)
```

The use *subplot* MATLAB command is used to hold two horizontal
images. First is the 3D temperature field, starting with drawing the
black outline of the brake disk

```
subplot(1,2,1)
hold on
plot3(x, y, z,'k-')
plot3(x, -y, z,'k-')
plot3(xx, y,zz,'k-')
plot3(xx,-y,zz,'k-')
```

The *i:th* solution is selected as the only solution in *fea.sol.u*
(since *evalexpr* per default uses the solution at the last time
step), after which the temperature is evaluated along the radius at
the disk center line coordinate (*z=0*).

```
fea.sol.u = u(:,i);
T = evalexpr( 'T-273.15', [r;zeros(size(r))], fea );
```

Using the assumption that the solution is axisymmetric, one can
extrapolate the data all along the brake disk with the help of the
annular grid struct *g* created earlier. The MATLAB *patch* command is
used to plot the *x-z* temperature field

```
h = patch( 'faces', g.c', ...
'vertices', [g.p(1,:)' zeros(size(g.p,2),1) g.p(2,:)'], ...
'facevertexcdata', T, ...
'facecolor', 'interp', ...
'linestyle', 'none' );
```

Furthermore, the temperature for the original patch in the positive
and mirrored (negative) *z*-directions is also plotted

```
postplot( fea, 'surfexpr', 'T-273.15', 'colorbar', 'off' )
fea.grid.p(2,:) = -fea.grid.p(2,:);
postplot( fea, 'surfexpr', 'T-273.15', 'colorbar', 'off' )
fea.grid.p(2,:) = -fea.grid.p(2,:);
```

Lastly, a title is set, the color map range fixed, and a suitable viewing angle is chosen

```
title( 'Temperature' )
caxis( [cmin cmax] )
view(3)
axis off
axis tight
```

For the second subplot the idea is to follow the von Mieses stress as
a function of time for the three points prescribed in *rz*. Just as
for the temperature, the stress can be evaluated with the
`evalexpr`

command
where the stress expression *svm* has been defined earlier in the
*fea.const* field of the model *fea* struct

```
subplot(1,2,2)
hold on
grid on
if( i>1 ) % Skip first zero solution
st = [st evalexpr( '(svm)*1e-6', rz, fea )];
```

The stress is plotted as a function of time, with additional text and legends added for identification

```
plot( tlist(1:i), st(1,:) )
plot( tlist(1:i), st(2,:) )
plot( tlist(1:i), st(3,:) )
text( tlist(i), st(1,end), 'r = rd' )
text( tlist(i), st(2,end), 'r = (rd+Rd)/2' )
text( tlist(i), st(3,end), 'r = Rd' )
axis( [0 tmax 0 max(st(:))] )
end
xlabel( 'Time [s]' )
ylabel( 'von Mieses stress [MPa]' )
```

Finally, before closing the loop, a drawing update is forced with the
*drawnow* command, and optionally an *jpeg* image file is written out
and saved for later processing

```
drawnow
print( '-r200', '-djpeg', sprintf('img%03i.jpg',i) )
end
```

After all the MATLAB postprocessing has finished the images can easily be converted to a video with a suitable tool, such as for example ffmpeg with the command

```
ffmpeg -i img%03d.jpg -c:v libx264 -vf "fps=25, format=yuv420p, crop=1600:1198:0:0" out.mp4
```

From the generated video one can now clearly see that the temperature
is the highest on the outer two-thirds of the disk consistent with
where the brake pad is acting. In contrast the maximum stress is
achieved at the inner radius *r = rd* around *t = 3.0 s*, and is
significantly higher than at the two points measured further out on
the disk.