On the determination of the quasi-static evolution of brittle plane cracks via stationarity principle

The crack front evolution in brittle solids is commonly modelled by defining some crack increment criterion, which can be derived from considerations on the stress singularity, from the definition of a dissipative potential, from the introduction of phenomenological concepts such as the crack mobility, and so on. In this work, we faced the problem with no allowance for any crack increment criterion, but using only the elastic properties, the fracture energy, and a stationarity principle. We will show that these ingredients are enough for determining the equilibrium and the quasi-static evolution of generally shaped three-dimensional brittle plane cracks. In doing this, we pointed out some new insight on the crack front motion, a set of new, generalised, domain integrals for measuring the pointwise crack ‘tension’, and a rigorous calculation of the intersection angle between the crack front and the free surface.