Three dimensional fracture growth as a standard dissipative system: some general theorems and preliminary numerical analysis.
Alberto Salvadori (University of Brescia / TUe), Francesca Fantoni (University of Brescia, Italy)
Crack initiation and growth: methods, applications, and challenges
Tue 9:00 - 10:30
Sayles Auditorium
The crack propagation problem for linear elastic fracture mechanics has been studied by several authors exploiting its analogy with standard dissipative systems theory. In recent publications minimum theorems were derived in terms of crack tip “quasi static velocity” for two-dimensional fracture mechanics. They were reminiscent of Ceradini’s theorem in plasticity. Following the cornerstone work of Rice on weight function theories, Leblond and coworkers proposed asymptotic expansions for Stress Intensity Factors (SIFs) in three dimensions. As formerly in 2D, expansions can be given a Colonnetti’s decomposition interpretation. In view of the expression of the expansions proposed however, symmetry of Ceradini’s theorem operators was not evident and the extension of outcomes proposed in 2D 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. Their performance is here presented within a set of classical benchmarks.