Modeling the Biaxial Behavior of Concrete by Damage Mechanics with Poisson’s Ratio Variable

A new model is introduced, for predicting the nonlinear behavior of the concrete until the rupture. The non-linear behavior of the concrete is taken into account under monotonic load verifying the principles of the mechanics damage [1] and the concepts of the mechanics of the fracture, using the foundations of the continuum mechanics of materials [2]. The nonlinear mechanical behavior of the concrete in unidirectional is described by two laws (Sargin [3] for the compression and Grelat [4] on the tension). By introducing two variables of damage applied in unidirectional respectively in tension and in compression (Y. Bouafia , R. Smahi, and al., (2014)) [5]. Their combination with the laws of the continuum mechanics of materials (Hooke’s low generalized) [2], and the theory of the mechanics damage (theory of the isotropy of the damage, and principle of the equivalent deformation), brings us to a law of variation of the damage in three-directional applied in bidirectional. In addition, if the variation of the Poisson’s ratio of concrete in unidirectional compression has attracted the interest of several researchers we can cites: (Sami, A., Klink, 1975 [6], Murray D.W. 1979 [7], Niels Saabye ottosen, (1980) [8], Atheel E. Allos., L.H.Martin, (1981) [9], Ramtani.S, Y. Berthaud , J. Mazars, (1992) [10] and Ferretti, E., (2004) [11]. For the three-dimensional, we can mention: Chen 1982 [12], Guo 1997 [13], Zhu 1998 [14], Hyuk-Chun Noh, Hyo-Gyoung Kwak 2006 [15] and Ding Faxing Yu Zhiwu 2006 [16]. Confrontations of the calculations with experimental results (behavior of the concrete in biaxial compression and tension) have allowed to describe and to follow the real behavior of the concrete.