Issue 18

S. Marfia et alii, Frattura ed Integrità Strutturale, 18 (2011) 23-33 ; DOI: 10.3221/IGF-ESIS.18.03 24 external surface of the quasi-brittle material; this collapse behavior is due to the fact that the tensile and shear strength of the glue used to apply the FRP to the support is generally greater than the strength of the concrete or masonry support. From this observation, it can be deduced that the body damage and the interface damage cannot evolve independently one from the other; in other words, their evolution is coupled [10]. In the present work, a new model of the FRP-concrete or masonry interface, that takes into account the coupling occurring between the degradation of the cohesive support material and the FRP detachment, is presented. A nonlocal damage and plasticity model is developed for the cohesive support material. An interface model which accounts for the mode I, mode II and mixed mode of damage and for the unilateral contact and friction effects is developed. Two different ways of performing the coupling between the body and the interface damage are proposed. Both the approaches assume that the interface damage is influenced not only by the detachment stresses but also by the body damage computed on the bond surface. The first approach ensures that the interface damage is not lower than the body damage evaluated at the bond surface [11]. The second approach is based on simplified micromechanical considerations. Some numerical applications are performed in order to assess the performances of the proposed coupled interface models in reproducing the mechanical behavior of the masonry elements strengthened with external FRP reinforcements. A COUPLED BODY - INTERFACE DAMAGE MODEL he structural system, schematizing the FRP reinforced concrete or masonry element, is studied in the framework of two-dimensional plane stress elasticity, considering small strain and displacement regime. The system, consists in three subsystems: the body 1  , modeling the concrete or masonry element, characterized by a cohesive constitutive law; the body 2  , modeling the FRP reinforcement, characterized by a linear elastic behavior; the interface  , modeling the connection between the reinforcement and the cohesive support material, characterized by a damaging behavior with friction and unilateral contact effects. In particular, the interface  is assumed to be constituted by three layers:  the glue, whose mechanical properties are generally much better than those of the support cohesive material;  a thin layer of the support cohesive material in which, during the application of the reinforcement, the glue penetrates the pores, improving its mechanical properties;  a further thin layer of the support cohesive material in which the detachment process occurs. Indeed, the first two layers remain joined to the FRP after the complete detachment of the reinforcement. The interface damaging process, occurring in the third layer, can be due to the stress induced by the detachment action and also by the degradation of the support cohesive material. As a consequence, the damage occurring in the body 1  influences the behavior and the detachment process of the interface. On the contrary, it can be assumed that the damage of the third layer, generated by the detachment stresses, remains localized in the interface, i.e. it does not influences the body damage. In order to take into account these two possible damaging effects, an interface coupled damage model should be adopted. In fact, the coupling ensures that the damage evolution in the interface depends on the body damage and not vice-versa. The constitutive laws of the body 1  , of the interface  , neglecting the coupling between the body and the interface damage, and of the new proposed interface  , considering two different ways of coupling the body and interface degradation, are presented in the following. Body nonlocal damage model for the cohesive material A plastic nonlocal damage model, characterized by the following constitutive law, is considered for the body 1  :         (1 ) sgn ( ) (1 )(1 sgn ( ) t c D H tr D H tr                σ σ e e (1) with  σ the stress tensor, t D  and c D  the damage variables in tension and in compression, respectively, the symbol sgn( )  indicating the sign of the variable  ,   H  the Heaviside function, i.e.   1 H   if 0   , otherwise   0 H   , and  σ the effective stress defined as:   p          σ C ε ε C e (2) T