Three-dimensional fracture growth as a standard dissipative system: some general theorems and numerical simulations

Abstract 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. Nguyen (1994); Bourdin et al. (2008); Salvadori (2008)). In recent publications (Salvadori and Carini (2011); Salvadori and Fantoni (2013)) minimum theorems were derived in terms of crack tip “quasi static velocity” for two-dimensional fracture mechanics. They were reminiscent of Ceradini's theorem (Ceradini (1966)) in plasticity. Following the cornerstone work of Rice (Rice (1989)) on weight function theories, Leblond and coworkers (Leblond (1999); Leblond et al. (1999)) proposed asymptotic expansions for Stress Intensity Factors (SIFs) in three dimensions. As formerly in 2D, expansions can be given a Colonnetti's decomposition interpretation (Colonnetti (1950)). In view of the expression of the expansions proposed in (Leblond (1999); Leblond et al. (1999)) however, symmetry of Ceradini's theorem operators was not evident and the extension of outcomes proposed in (Salvadori and Fantoni (2013)) not straightforward. Following a different path of reasoning, minimum theorems have been finally derived. Moving from well established theorems in plasticity, algorithms for crack advancing have been formulated (Salvadori and Fantoni (2014,a); Salvadori and Fantoni (2014,b)). Their performance is here presented within a set of classical benchmarks.