All the previous chapters have treated the behaviour of a volume element by considering it as a continuous medium, represented by its state variables. The theory of cracking phenomena or fracture mechanics describes the behaviour of solids or structures with macroscopic geometric discontinuities at the scale of the structure. These discontinuities are line discontinuities in two-dimensional media (such as plates and shells) and surface discontinuities in three-dimensional media. The theory of damage can be used to predict the onset of a macroscopic crack. The theory of cracking phenomena, on the other hand, can be used to predict the evolution of the crack up to a complete failure of the structure.

In structural analysis these discontinuities must be taken into consideration as they modify the stress, strain and displacement fields on such a scale that the assumption of a homogeneous medium would no longer be meaningful. The theory of damage can also be used to study the evolution of cracks, as shown in Section 8.6.4, but more global methods allow consideration of these problems in a more synthetic and simplified way at least for quite simple structures and loads.

As early as 1920, Griffith showed that the failure of a brittle elastic medium could be characterized by a variable, later called the energy release rate, whose critical value, independent of the geometry of the structure, was a characteristic of the material.