Minimum energy multiple crack propagation. Part I: Theory and state of the art review. (15th March 2018)

• Record Type: Journal Article
• Authors: Sutula, Danas; Kerfriden, Pierre; van Dam, Tonie; Bordas, Stéphane P.A.
• Is Part Of: Engineering fracture mechanics. Volume 191(2018)
• Page Start: 205
• Page End: 224
• Publication Date: 2018-03-15
• Subjects: Fracture mechanics -- Periodicals; Rupture, Mécanique de la -- Périodiques; Fracture mechanics; Periodicals; 620.112605
• DOI: 10.1016/j.engfracmech.2017.07.028
• Languages: English
• ISSNs: 0013-7944

Abstract

Highlights: The problem of multi-crack growth is posed as a minimum total energy problem, which naturally follows from Griffith's law. Competing crack growth is resolved by solving a constrained quadratic optimization problem. Three solution strategies are proposed for different cases of fracture stability in order to resolve competing crack growth efficiently. The crack extension direction is determined using a criterion of vanishing energy dissipation rate with respect to the rotation of a crack tip extension. Our Matlab codes, including documentation, benchmark and example cases, are available open-source as supplementary material. Abstract: The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith's theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. The key contributions of Part-I of this three-part paper are given as follows. (1) Formulation of the total energy functional governing multiple crack behaviour. (2) Three solution methods to the problem of competing crack growth for different fracture front stabilities, e.g. stable, unstable, or partially stable crack tip configurations; we compare our approach to Budyn et al. (2004) and demonstrate via example cases that the latter approach of resolving competing crack growth is not energy minimal in some cases. Finally, (3), the minimum energy criterion for a set of crack tip extensions is posed as the condition of vanishing rotational dissipation rates with respect to the extension angles. The proposed formulation lends itself to a straightforward application within a discrete framework involving multiple finite-length crack tip extensions. The open-source Matlab code, documentation, benchmark/example cases are included as supplementary material.