  We present a phase field model of the propagation of fracture under plane
strain. This model, based on simple physical considerations, is able to
accurately reproduce the different behavior of cracks (the principle of local
symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition,
we test our model against recent experimental findings showing the presence of
oscillating cracks under bi-axial load. Our model again reproduces well
observed supercritical Hopf bifurcation, and is therefore the first simulation
which does so.
