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. © 2011 Elsevier Ltd. All rights reserved.
Salvadori, A., & Carini, A. (2011). Minimum theorems in incremental linear elastic fracture mechanics. International Journal of Solids and Structures, 48(9), 1362–1369. https://doi.org/10.1016/j.ijsolstr.2011.01.019