The virtual crack extension method is a way to compute the energy release rate for a crack. The idea in the virtual crack extension method is to evaluate the change in total energy when the surface area of a crack is changed, but without actually solving for different geometries. Several different variants on this theme can be found in the literature.
where U is the total potential energy, and
A is an increase in crack area. The total potential energy consists of the strain energy and the potential of the loads.
Here A(
s) is some kind of local crack area. The new area that is created by a small crack growth must be located in the plane of the crack, and by extending the crack perpendicular to the crack front. If
s is the tangent to the crack front, and
n(
s) is the local normal to the crack face, then the local crack extension direction is
Here, r is the distance from the crack tip in the plane perpendicular to the crack tip.
Rs is the radius of the sensitivity region, which can be given by the user. The control variable field for the sensitivity analysis is denoted
c(
s).
where Ac is the area of the crack.