Modeling Cracks
A crack in a solid model can be represented in two fundamentally different ways:
•
As an ideal crack, that is by a single boundary. Across this boundary, the displacement field is discontinuous. Using COMSOL nomenclature, this is called a
slit condition
.
•
By its true geometry, in which case the two sides of the crack are two different boundaries. In the true geometry, the two crack surfaces may coincide, or there may be a distance between them.
Both cases have an analogous representation in a symmetry plane. The ideal crack is just a boundary located in the symmetry plane, but without the symmetry conditions, so that it can open. This can however just as well be considered as special case of a geometrical crack, so in symmetry planes the distinction more or less disappears.
Fundamental for cracks is that the stress and strain states at the crack tip are singular, so any mesh refinement will only produce even higher stresses. For a linear elastic material, the stresses and strains in the vicinity of the crack vary as
, where
r
is the distance from the crack tip.
, where r is the distance from the crack tip.