Crack Paths 2006

4. T H EP E R F O R A TSETDR U C T U R E

In order to merge the cylinder and the uncracked structure, the intersection points have to be

calculated. These are points where edges of the cylinder triangulation are cut by triangles of

the uncracked structure, and vice versa. These points are part of the intersection line between

the two triangulations. All triangles that are crossed by the intersection line have to be

remeshed in order to maintain a consistent triangulation. The edges of the cut triangles and the

intersection line must be part of the new triangulation, see Figure 4. Routines for remeshing

the crossed triangles are based on the Delaunay triangulation algorithms by Paul-Louis

George [4].

Figure 4. Remeshing of intersected triangles, before remeshing (above) and after

remeshing (below).

Figure 5a shows the cylinder and the uncracked structure after remeshing. Now, the parent

triangles and any other superfluous triangles must be deleted. Superfluous triangles are

triangles of the uncracked structure inside the cylinder triangulation (marked red in Figure 5)

and cylinder triangles outside the triangulation of the uncracked structure (blue). This is even

clearer in Figure 5b, where all triangles not cut by the cylinder were removed.

Which triangles are superfluous is determined by the intersection points and the orientation

of the triangles. The convention is such that a triangle, when observed from the outside, has a

normal vector pointing outwards as a result of its counter-clockwise positive orientation.

The resulting triangulation is the so-called perforated structure, Figure 6.

Figure 5. The remeshed triangles and any superfluous triangles have to be deleted after

remeshing. a) The perforated structure plus superfluous triangles. b) Same

view with triangles not involved in the cutting removed.