Issue 31

A. Abrishambaf et alii, Frattura ed Integrità Strutturale, 31 (2015) 38-53; DOI: 10.3221/IGF-ESIS.31.04 46 (a) (b) Figure 11 : Three-dimensional view of numerical model [24]: (a) geometry, constraints and prescribed displacement, (b) finite element mesh. Concrete constitutive model The concrete damage plasticity, CDP, model was used to simulate the mechanical performance of concrete because it is proficient to model the cracking of concrete in tension and crushing in compression. On the other hand, this model uses the concept of isotropic damage elasticity in combination with isotropic compression and tension plasticity to simulate the inelastic behaviour of concrete under compressive and tensile stresses. The CDP model uses a yield surface that is defined as the loading function proposed by Lubliner et al. [26]. The evaluation of the yield surface is controlled by two hardening variables, namely, the plastic strain in tension ( pl t   ) and the plastic strain in compression ( pl c   ). In the case of the effective stress, the yield function is determined as follow:       max max 1 3 1 ˆ ˆ pl pl c c F q p                  (4) where:     0 0 0 0 1 2 1 b c b c         , 0 0.5    (5)         1 1 pl c c pl t t              (6)   3 1 2 1 c c k k     (7) In these equations, p and q are two stress invariants of the effective stress tensor, namely, the hydrostatic stress and the Von Mises equivalent effective stress, respectively, max ˆ  stands for the maximum principal effective stress and is the algebraic maximum eigen value of the effective stress  [27], x represents Macauley bracket   1 2 x x   , 0 0 b c   is the ratio between the initial biaxial compressive strength and the initial uniaxial compressive strength, ( ) pl t t    and ( ) pl c c    are the effective tensile and compressive cohesive stresses, respectively. Parameter c k is physically assumed as a ratio of the distances between, respectively, the compressive meridian and the tensile meridian with hydrostatic axis in the deviatoric cross section. If this ratio tends to 1, the deviatoric cross section of the failure surface becomes a circle similar to the Drucker – Prager yielding surface. However, definition of this parameter is only possible if the full triaxial compressive tests are executed on concrete specimens [28]. Tab. 3 includes the adopted initial parameters for the CDP model used to simulate the response of the splitting tensile tests. prescribed displacement flush part notch part