Minimum theorems in incremental linear elastic fracture mechanics

The crack propagation problem for linear elastic fracture mechanics has been studied by several authors exploiting its analogy with standard dissipative systems theory (see e.g. (Nemat-Nasser et al., 1980, Nguyen, 2000, Maugin, 1992, Bourdin et al., 2008 and Salvadori, 2008). This approach is here further advanced, by noting that Stress Intensity Factors (SIFs) asymptotic expansion (Amestoy et al., 1986 and Amestoy and Leblond, 1992) enjoys a Colonnetti’s decomposition (Colonnetti, 1918 and Colonnetti, 1950) interpretation. As a consequence, minimum theorems are derived in terms of crack tip “quasi static velocity”. They are reminiscent of Ceradini’s theorem (Ceradini, 1965 and Ceradini, 1966) in plasticity.