Experimental study and analytical formulation of mechanical behavior of concrete Xudong Chen, Shengxing Wu ⇑ , Jikai Zhou College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China highlights  Mechanical behavior of normal concrete was tested and analyzed.  Strain at peak stress increases with an increase in concrete strength.  Existing expressions relating elastic modulus and strength is discussed.  A mathematical model was developed for predicting stress–strain curves.  Suitability of existing models for stress–strain curves is assessed. article info Article history: Received 15 February 2013 Received in revised form 22 April 2013 Accepted 4 May 2013 Available online 10 June 2013 Keywords: Concrete Mechanical behavior Experimental study Modeling abstract An experimental investigation was carried out to generate the mechanical behavior of normal concrete cores with a strength range of 10–50 MPa, including the compressive strength, elastic modulus, strain at peak stress and stress–strain relationships. From several formulations for concrete in this study, it was observed that a conservative estimation of the elastic modulus and strain at peak stress can be obtained from the value of compressive strength. The accuracy of predictions of a number of analytical models available in the literature is discussed. This paper shows the development of a statistical damage mechanics model for concrete at uniaxial loading in compression to ultimate failure. This model is formu- lated by using Weibull’s statistical theory of the strength of materials. The body of heterogeneous concrete material is simulated as a continuum comprising a large population of microscopic ‘‘weakest- link’’ elements. This model provides a good prediction of experimental results in this study. When compared other existing models, it gave better prediction. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Reinforced concrete is widely used to build infrastructures in many countries. The main constituent materials of reinforced con- crete structures are plain concrete and steel bars. The concrete is essential to carry compressive stresses, however, the steel is essen- tial to transmit tensile stresses. The discussion of instantaneous deformations of concrete under load is timed from a theoretical viewpoint because deformations provide indirect information con- cerning the internal structure as well as the failure mechanism of concrete [1]. From a practical standpoint, the ultimate strength de- sign of reinforced concrete elements brought the stress–strain rela- tionship into focus. Also, a knowledge of the deformability of concrete is necessary to compute deflections of structures, to com- pute stresses from observed strains, to design sections of highway slabs, and to compute loss of pre-stress in pre-stressed members [2,3]. The stress–strain curves of concrete are dependent on two ma- jor parameters; testing conditions and concrete characteristics. Testing conditions include variables such as stiffness of testing ma- chine [4–6], shape and size of the specimen [7,8], strain rate [9– 11], type of strain gauge and gauge length [6,12]. Concrete charac- teristics depend on many interrelated variables such as water–ce- ment ratio [13,14], the mechanical and physical properties of the cement [15,16] and aggregate [17,18], and the age of the specimen when tested [19,20]. The evaluation of such parameters based on one series of test results may not be accurate for another series of experiments under different conditions. The nonlinear behavior of the stress–strain relation of concrete is well known. Many inves- tigators have tried to represent the relationship by standard math- ematical curves, e.g., a parabola, hyperbola, ellipse, cubic parabola, or combinations like parabola with a straight line or a sine wave with a cubic parabola and so on [21,22]. Some researchers have approximated the stress–strain curve into a triangle, a rectangle 0950-0618/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2013.05.041 ⇑ Corresponding author. Tel.: +86 25 83786551; fax: +86 26 83786986. E-mail address: sxwuhhu@hotmail.com (S. Wu). Construction and Building Materials 47 (2013) 662–670 Contents lists available at SciVerse ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat