Phase-field modeling of fracture for quasi-brittle materials Jacinto Ulloa a,b,⇑ , Patricio Rodrı ´guez c,d , Cristo ´ bal Samaniego e , Esteban Samaniego f,b a Department of Civil Engineering, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium b Departamento de Recursos Hı ´dricos y Ciencias Ambientales, Universidad de Cuenca, Cuenca 010151, Ecuador c Universidad de Cuenca, Cuenca 010151, Ecuador d Institut fu ¨ r Kontinuumsmechanik, Leibniz Universita ¨ t Hannover, Hannover 30167, Germany e Inria Bordeaux – Sud-Ouest Research Center, 200 Avenue de la Vieille Tour, Talence 33405, France f Facultad de Ingenierı ´a, Universidad de Cuenca, Ecuador Received 30 March 2018; received in revised form 23 July 2018; accepted 12 August 2018 Available online 26 October 2018 Abstract This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topol- ogy. Within the computational mechanics community, several studies have treated the issue of modeling fracture using phase fields. Most of these studies have used an approach that implies the lack of a damage threshold. We herein explore an alternative model that includes a damage threshold and study how it compares with the most popular approach. The formulation is systematically explained within a rigorous variational framework. Subsequently, we present the corresponding three-dimensional finite element discretization that leads to a straightforward numerical implementation. Benchmark simulations in two dimensions and three dimensions are then presented. The results show that while an elastic stage and a damage threshold are ensured by the present model, good agreement with the results reported in the literature can be obtained, where such features are generally absent. Ó 2018 Tongji University and Tongji University Press. Production and hosting by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Quasi-brittle materials; Fracture; Variational formulation; Phase fields; Gradient damage 1 Introduction Crack initiation and propagation in quasi-brittle materi- als is both of significant scientific interest and paramount importance in engineering applications. Examples of these materials include concrete and rocks that exhibit microc- racks that localize in narrow bands (Comi, 1999). Methods developed in the framework of classical fracture mechanics, typically rooted in the pioneering works of Griffith (1921), Irwin (1957) and Barenblatt (1962), have been relatively successful in several engineering applications. Nevertheless, these theories present major limitations, including the inability to naturally describe crack initiation and propaga- tion without initial defects and a prescribed crack path (Francfort & Marigo, 1998). Moreover, their application requires nontrivial finite element techniques such as local refinement near the crack tip (Nguyen-Xuan, Liu, Bordas, Natarajan, & Rabczuk, 2013). In view of these drawbacks, a variety of methods have emerged in the past few decades with the objective of providing a more conve- nient description of fracture. From a continuum mechanics perspective, the study of post-critical behavior in solids can be approached using softening constitutive models. This leads to strain localiza- tion, which signals the appearance of the so-called fracture process zone. Thus, some form of representation of the https://doi.org/10.1016/j.undsp.2018.08.002 2467-9674/Ó 2018 Tongji University and Tongji University Press. Production and hosting by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). ⇑ Corresponding author at: Department of Civil Engineering, Katho- lieke Universiteit Leuven, B-3001 Leuven, Belgium. E-mail addresses: [email protected] (J. Ulloa), patricio. [email protected] (P. Rodrı ´guez), cristobal.samaniego-alvara- [email protected] (C. Samaniego), [email protected] (E. Samaniego). www.elsevier.com/locate/undsp Available online at www.sciencedirect.com ScienceDirect Underground Space 4 (2019) 10–21
Phase-field modeling of fracture for quasi-brittle materials
Jun 16, 2023
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Related Documents
