Crack nucleation in negative geometries

The failure behaviour of structural situations depends on the shape of the energy release rate function of possible crack configurations. Depending on the structural situation, the energy release rate function can decrease (negative geometry) or increase (positive geometry) with increasing crack size. In this work, three structural situations exhibiting locally positive and locally negative behaviour are analysed using a coupled stress and energy criterion in the framework of Finite Fracture Mechanics. The nucleation and stability of finite cracks is discussed in detail. Exact and approximate solutions for the stress fields and the stress intensity factors are employed or newly derived to allow for a closed-form solution of the failure model. For the considered configurations, it is identified whether the nucleated cracks are stable or unstable.