Physical significance of the curvature varifold-based description of crack nucleation

The nucleation and/or growth of cracks in elastic-brittle solids has been recently described in [M. Giaquinta , P. M. Mariano, G. Modica , D. Mucci (2010), Ground states of simple bodies that may undergo brittle fracture, Physica D - Nonlinear Phenomena, 239, 1485-1502.] in terms of a special class of measures and with a variational technique requiring the minimization of a certain energy over classes of bodies. Here, the physical foundations of the theory and the basic ideas leading to it are described and commented further on. A view on certain possible developments and shifts toward different settings is also given. This article has expository character.