Issue 31

H.F.S.G. Pereira et alii, Frattura ed Integrità Strutturale, 31 (2015) 54-66; DOI: 10.3221/IGF-ESIS.31.05 58 29]. In a second stage, a similar local bond stress – slip law to that proposed by [27] was also used. In order to implement it in the software, it was needed to perform previously a transformation of the bond stress – slip law to a damage – slip relationship. Figure 7 : Linear bond-slip law [26]. With reference to the Fig. 7, the first part of the constitutive law is linear elastic up to the maximum bond stress (point A), involving an initial displacement 0 n  . At this point the interface starts to become damaged. Once the maximum bond stress is reached and the crack begins to propagate, the stress starts to reduce up to the maximum displacement 1 n  (point B). G c is the fracture energy needed to propagate the interfacial crack. Concrete and steel constitutive behaviour Regarding the mechanical behaviour of the steel rebar, it was assumed an elastic perfectly-plastic behaviour. On the other hand, to model the concrete behaviour two distinct approaches with different levels of complexity were adopted. It was assumed a linear elastic behaviour and nonlinear behaviour by using the Concrete Damage Plasticity (CDP) model comprised in the ABAQUS software [26]. The CDP model from the ABAQUS library [26] considers the total strain decomposed into an elastic ( el  ) and plastic ( pl  ) strain components, el pl      . The stress-strain relation associated with the damage evolution is given by:     0 1 el pl d D       (6) where d is the damage variable ( d = 0 no damage, d = 1 fully damaged) and 0 el D is the non-damaged elastic modulus. Damage is associated with the typical degradation mechanisms of concrete – cracking in tension and crushing in compression, which involves a decrease of the elastic modulus. Damage is governed by the hardening variables pl  ~ and the effective stress   , pl d d     . The hardening variables under compression ( pl c  ~ ) and tension ( pl t  ~ ) are considered independently. Figure 8 : Yield surface of DCP model [26].