Crack propagation simulation without crack tracking algorithm : embedded discontinuity formulation with incompatible modes

Stanić, Andjelka (author), Brank, Boštjan (author), Ibrahimbegović, Adnan (author), Matthies, Hermann G. (author)

We show that for the simulation of crack propagation in quasi-brittle, two-dimensional solids, very good results can be obtained with an embedded strong discontinuity quadrilateral finite element that has incompatible modes. Even more importantly, we demonstrate that these results can be obtained without using a crack tracking algorithm. Therefore, the simulation of crack patterns with several cracks, including branching, becomes possible. The avoidance of a tracking algorithm is mainly enabled by the application of a novel, local (Gauss-point based) criterion for crack nucleation, which determines the time of embedding the localisation line as well as its position and orientation. We treat the crack evolution in terms of a thermodynamical framework, with softening variables describing internal dissipative mechanisms of material degradation. As presented by numerical examples, many elements in the mesh may develop a crack, but only some of them actually open and/or slide, dissipate fracture energy, and eventually form the crack pattern. The novel approach has been implemented for statics and dynamics, and the results of computed difficult examples (including Kalthoff’s test) illustrate its very satisfying performance. It effectively overcomes unfavourable restrictions of the standard embedded strong discontinuity formulations, namely the simulation of the propagation of a single crack only. Moreover, it is computationally fast and straightforward to implement. Our numerical solutions match the results of experimental tests and previously reported numerical results in terms of crack pattern, dissipated fracture energy, and load–displacement curve.

• Language: English
• Keywords: fracture modelling, quadrilateral finite element, embedded strong discontinuity, incompatible mode method, rigid-damage softening, dynamic fracture
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: 39 str.
• Numbering: Vol. 386, art. 114090
• PID: 20.500.12556/RUL-131840
• UDC: 624.074.4
• ISSN on article: 0045-7825
• DOI: 10.1016/j.cma.2021.114090
• COBISS.SI-ID: 73902083
• Publication date in RUL: 04.10.2021

STANIĆ, Andjelka, BRANK, Boštjan, IBRAHIMBEGOVIĆ, Adnan and MATTHIES, Hermann G., 2021, Crack propagation simulation without crack tracking algorithm : embedded discontinuity formulation with incompatible modes. Computer methods in applied mechanics and engineering [online]. 2021. Vol. 386, no. 114090. [Accessed 17 April 2025]. DOI 10.1016/j.cma.2021.114090. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=131840

Record is a part of a journal

• Title: Computer methods in applied mechanics and engineering
• Shortened title: Comput. methods appl. mech. eng.
• Publisher: Elsevier
• ISSN: 0045-7825
• COBISS.SI-ID: 6695685

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: modeliranje loma materiala, četverokotni končni element, vstavljena močna nezveznost, nekompatibilni pomiki, mehčanje, dinamična odpoved materiala

Projects

• Funder: Deutsche Forschungsgemeinschaft
• Project number: MA 2236/28-1

• Funder: ARRS - Slovenian Research Agency
• Project number: J2-1722
• Name: Numerično modeliranje širjenja razpok v krhkih in duktilnih konstrukcijah