Issue 31

A. Abrishambaf et alii, Frattura ed Integrità Strutturale, 31 (2015) 38-53; DOI: 10.3221/IGF-ESIS.31.04 47 Dilatation angle [degrees] 40 Eccentricity, e [-] 0.1 σ bo /σ co [-] 1.16 K c [-] 0.667 Table 3 : The constitutive parameters of CDP model. Concrete constitutive model: Stress – strain relationship for modeling the SFRSCC uniaxial compressive behaviour In CDP model, once the concrete compressive strength ( cu cm f   ) attained, the concrete shifts to the non-linear phase. Then, the compressive inelastic strain, in c   , is defined by subtracting the elastic strain component, 0 el c  , from the total strain, c  , in the uniaxial compressive test. 0 in el c c c       (8) 0 0 el c c E    (9) In the CDP model, from the stress – inelastic strain relationship ( in c c     ) that is provided by the user, the stress versus strain response ( c c    ) can be converted to the stress – plastic strain curve ( pl c c     ) automatically by the software. Tab. 4 includes the values of the model parameters used in the numerical simulation of the splitting tensile tests. Density, ρ 2.4×10 6 N/mm 3 Poisson ratio, υ 0.2 Initial young modulus, cm E 34.15 N/mm 2 Compressive strength, cm f 47.77 N/mm 2 Tensile strength Inverse analysis Post-cracking parameters Inverse analysis Table 4 : Mechanical properties adopted in the numerical simulations. Concrete constitutive model: Stress – strain relationship for modeling the SFRSCC uniaxial tensile behaviour The stress – strain response under uniaxial tension had a linear elastic behaviour until the material tensile strength ( 0 t  ) was attained. Afterward, the tensile response shifted to the post-cracking phase where a non-linear response was assumed. The SFRC post-cracking strain, ck t   , can be determined by subtracting the elastic strain, 0 el t  , corresponding to the undamaged part from the total strain, t  : 0 ck t el t t       (10) 0 0 el t t E    (11) From the stress – cracking strain response ( ck t t     ) defined by the user, the stress – strain curve ( t t    ) was converted to a stress – plastic strain relationship ( pl t t     ). Inverse analysis procedure The σ i and w i values that define the tensile stress – crack width law were computed by fitting the numerical load – crack width curve to the correspondent experimental average curve. From the nonlinear finite element analysis, the numerical load – crack width response, F NUM – w , was determined, and compared to the experimental one, F EXP – w. At last the normalized error, err , was computed as follows: