Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model

• Published in: Computer methods in applied mechanics and engineering 2018-10, Vol.340, p.480-499
• Main Authors: Nikolić, Mijo, Do, Xuan Nam, Ibrahimbegovic, Adnan, Nikolić, Željana
• Format: Article
• Language: English
• Subjects: Algorithms; Coalescing; Computer simulation; Crack initiation; Crack propagation; Cracks; Damage free energy; Dynamic crack propagation; Dynamics; Embedded strong discontinuities; Finite element method; Fracture mechanics; Fracture toughness; Kinetic energy; Kinetics; Laws; Localized failure; Mechanics; Mechanics of materials; Physics; Plastic free energy; Strain analysis; Strain energy; Time integration; Timoshenko beams; Tracking
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2018.06.012

In this work we propose and compare the two models for crack propagation in dynamics. Both models are based on embedded strong discontinuities for localized cohesive type crack description and both provide the advantage to not to require tracking algorithms. The first one is based on discrete lattice approach, where the domain is discretized with Voronoi cells held together prior to crack occurrence by cohesive links represented in terms of Timoshenko beams. The second one is based on constant strain triangular solid element. In both models, propagation of cracks activates enhancements in the displacement field leading to embedded strong discontinuities. The latter remain localized inside the element, regulated by the localized traction separation behavior defined through exponential softening law. Thus, the both models provide the result that remain mesh-independent, with fracture energy as the model parameter. We show that implementation in dynamics framework can be obtained by adding inertial effects without modifying the existing quasi-statics models. In order to provide reliable results, classical implicit Newmark algorithm can be used for time integration. The two presented models are subjected to dynamic crack propagation benchmarks, where detailed analysis on strain, kinetic, plastic free and dissipated energy during simulation is verified by comparison to the amount of total work which is introduced into the system. The main strength of the proposed approach is that cracks initiation, propagation, their coalescence, merging and branching are automatically obtained without any tracking algorithms. In addition, since the discontinuities remain localized inside elements, accurate results can be obtained even with coarser grids, leading to efficient methodology capable of capturing complex crack patterns in dynamics.