Available online at www.sciencedirect.com ScienceDirect Comput. Methods Appl. Mech. Engrg. 386 (2021) 114090 www.elsevier.com/locate/cma Crack propagation simulation without crack tracking algorithm: Embedded discontinuity formulation with incompatible modes A. Stani´ c a ,∗ , B. Brank b , A. Ibrahimbegovic c , H.G. Matthies d a University of Twente, Faculty of Engineering Technology, The Netherlands b University of Ljubljana, Faculty of Civil and Geodetic Engineering, Slovenia c Université de Technologie de Compiègne - Alliance Sorbonne Universités, Laboratoire de Mécanique, France d Technische Universität Braunschweig, Institute of Scientific Computing, Germany Received 16 December 2020; received in revised form 7 July 2021; accepted 30 July 2021 Available online 23 August 2021 Abstract 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. c ⃝ 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Fracture modelling; Quadrilateral finite element; Embedded strong discontinuity; Incompatible mode method; Rigid-damage softening; Dynamic fracture 1. Introduction The strong discontinuity approach (SDA) is a well established method [1–18] for modelling crack propagation in quasi-brittle materials (such as concrete, high strength steel, and rock). In this work, we focus on the devel- opment of a corresponding quadrilateral finite element with a statically and kinematically optimal non-symmetric formulation [19]. ∗ Corresponding author. E-mail address: [email protected] (A. Stani´ c). https://doi.org/10.1016/j.cma.2021.114090 0045-7825/ c ⃝ 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Crack propagation simulation without crack tracking algorithm: Embedded discontinuity formulation with incompatible modes
Jun 04, 2023
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