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

Abstract

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.

Determining Compressed Concrete Element Limit States Based on the Widths and Depths of Cracks Caused by Transverse Deformations

“…Studies of uniaxially compressed concrete specimen behavior in the transverse direction are usually limited to the elastic performance stage. In this stage, transverse deformations are generally determined by Poisson's coefficient [10][11][12][13]. Although many experimental investigations have been carried out to study concrete specimen behavior in the longitudinal direction, few of them have focused on transverse deformations out of the elastic limits.…”

Mesoscale Study on Dilation Behavior of Plain Concrete under Axial Compression

“…Klink studied the distribution of dilation at the section of a concrete specimen experimentally [11], and Allos investigated the influences of compressive strength and age on the dilation of concrete [12]. The volumetric strain of concrete was analyzed in Ferretti's study [13], which was used to describe the biaxial behavior of concrete using damage mechanics [14]. Although relevant studies have been carried out, no theoretical formula for the dilation of plain concrete has been put forward in the above literature.…”