Characterization of concrete specimen fracture response: 2D numerical study N. Trivedi ⁎, R.K. Singh, J. Chattopadhyay Reactor Safety Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India abstract article info Article history: Received 2 July 2014 Received in revised form 21 August 2014 Accepted 22 August 2014 Available online 20 September 2014 Keywords: Concrete Three point bend specimen Triangular and quadrilateral elements The reported investigations undertaken so far on concrete fracture involve limited tests on laboratory size concrete specimens and provide a basic understanding of the fracture phenomenon, but the precise quantification of fracture parameters is still elusive. Therefore purely an experimental approach is not preferably a practicable solution, rather it is important to invoke the systematic computational approach for evaluating the load-crack mouth opening dis- placement and load–load line displacement responses to characterize the concrete fracture phenomenon. While performing the numerical study of concrete components using finite element method, mesh sensitivity is an extremely important issue which is investigated in this paper, through detailed analysis of geometrically sim- ilar three point bend (TPB) beams having constant length to depth ratio. The finite element modeling of the TPB concrete beams performed by incorporating the fracture energy based softening model predicted the results that are found to be mesh insensitive. In the present finite element analysis, the performance of triangular elements is investigated and observed to be superior over the quadrilateral elements. This has been concluded based on the completeness of interpolation function and discretization technique, which is illustrated by simulating a number of benchmark problems of TPB concrete specimens. The efficient analytical procedures to predict the parameters required to characterize the concrete fracture phe- nomenon are explored. The simulation of TPB specimen yields the parameters, such as maximum load, vertical displacement at maximum load, load vs. load line displacement and load vs. crack mouth opening displacement responses which are required for epitomizing the concrete fracture behavior. The numerically observed response is found to be in excellent agreement in most of the cases with the reported literature. © 2014 Elsevier Ltd. All rights reserved. 1. Introduction As is well know that concrete is the most commonly used building material in the world because of their excellent shielding capability, fire rating, long service life under normal and accidental conditions and ease in construction with relatively lower cost. In-spite of such salient features, the concrete structures consist of numerous micro-cracks or inherent flaws. Under service loads, accidental load and exposure to regular envi- ronmental conditions, the micro-cracks might result in fracture (or macro-crack formation) of the concrete structures. As an outcome, the large complex cracking zone is formed. The cracking zone can be charac- terized by the toughening mechanism like micro-crack shielding, aggre- gate bridging, crack deflection, crack tip blunting, crack surface roughness induced closure and crack branching as shown in Fig. 1. The toughening mechanisms can be reasonably quantified by the dis- sipated energy during the fracture process of concrete. Due to anisotropic and heterogeneous nature of concrete, the cracking should be described through the energy criteria, instead of the strength criteria. Even though cracks play an important role, concrete structures have been successfully designed and built without any use of fracture mechanics. The risk in the current design practice for concrete is that inherent flaws in the material might grow under loading to unacceptable lengths. It is therefore imper- ative that necessary steps should be taken to enhance the current under- standing and improve the design practices associated with concrete in order to reliably account for the possible failure mechanisms which could be achieved by introducing the fracture mechanics concepts. The major reasons for the application of fracture mechanics to concrete are as follows [1–4]: (i) In a concrete structure the crack growth requires a certain amount of energy that can only be studied through an energy based propagation criterion. The fracture process in quasi- brittle material involves the material separation that is better de- scribed by energy principles than by stress or strain criterion. (ii) The finite element formulation based on limiting stress or strain criteria showed the dependency on mesh size. However by incor- porating the fracture criteria based concrete model in finite element analysis, the observed response is found to be free from mesh sensitivity. Structures 1 (2015) 39–50 ⁎ Corresponding author at: Scientific Officer, BARC, Engineering Hall-7, Room No-407, Trombay, Mumbai, India. Tel.: +91 22 25591548. E-mail addresses: ntwipro08@gmail.com, nehat@barc.gov.in (N. Trivedi). http://dx.doi.org/10.1016/j.istruc.2014.08.001 2352-0124/© 2014 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect Structures journal homepage: http://www.elsevier.com/locate/structures