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; Salvadori, 2008). This approach is here further advanced, by noting that Stress Intensity Factors (SIFs) asymptotic expansion (Amestoy et al., 1986; Amestoy and Leblond, 1992) enjoys a Colonnetti’s decomposition (Colonnetti, 1918; 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; Ceradini, 1966) in plasticity.