Plotting stress trajectories (principal stress lines)

The visualization of stress trajectories is not standard in FE-programs. It would be a valuable tool for tailored fiber placement (TFP) and added manufacturing (AM). For example, fiber courses, which follow the local principal stress directions, make use of the superior stiffness and strength of the fibers. This task can be done without any additional software within CalculiX for 2D plane stress problems:
A static calculation provides the principal stress (PS) directions, which serve as local systems for the orthotropic thermal conductivities k1 and k2 in the following heat conduction analysis. For extreme conditions with k1/k2 > 10E4 the isotherms are tangent to the PS1 directions: The isotherms of a heat conduction calculation with extreme orthotropy simulate the PS lines.

The input of the animated figure (disc with hole under tension) can be downloaded from:

CalculiX-Input and Fortran-Program for stress trajectories

Contents of Static.inp, Static-BulkData.inp, Local.for with compilation->, Local.exe, Heat.inp, Static.dat, Elset.inp, Solid.inp, Orientation.inp. The last 4 files are redundant, they were produced by CalculiX 2.16 (Windows 7 and 10) and Local.for (Local.exe). Due to this exe-File there may be a warning during the download process!

Visualization of stress trajectories can be done within 3 step:

A) Linear static run with calculation of stresses, use only *El Print, S; no *Node Print

B) Calculation of the maximum stress direction outside CalculiX (dat-file from A is Input for Local.exe ← Fortran program Local.for). This program produces 3 Files:

*Elset, Elset=E 1
*Elset, Elset=E 2
… and so on

*Solid Section, Material=Mat, Orientation=OR 1, Elset=E 1
*Solid Section, Material=Mat, Orientation=OR 2, Elset=E 2

*Orientation, Name=OR 1
1., 0., 0., 0., 1., 0.
3, -8.8512
*Orientation, Name=OR 2
1., 0., 0., 0., 1., 0.
3, -8.5523

for every element. Please note the blanks in the Elset- and Orientation-numbers. They are valid and ignored by Calculix.

C) Steady state heat transfer analysis (same mesh as in A) with local systems from B for every element and orthotropic conductivities k1 and k2.
The influence of the degree of orthotropy can be studied in the animation, k1 is doubled in every frame, whereas k2 is held constant. It can be seen that k1/k2 must be extreme to get the isothermal lines identical to the principal stress lines, e.g.:
1.E4, 1., 1.

Theory: Please look at:
Integration of Direction Fields with Standard Options in Finite Element Programs