N. Oudni et alii, Frattura ed Integrità Strutturale, 35 (2016) 278-284; DOI: 10.3221/IGF-ESIS.35.32 280 , 0 , 0, If f and f Then 0 0, 0 d h d With d else (8) The function h is detailed as follows: in order to capture the differences of mechanical responses of the material in tension and in compression, the damage variable is split into two parts: t t c c d d d (9) Where t d and c d are the damage variables in tension and compression, respectively. They are combined with the weighting coefficients t and c , defined as functions of the principal values of the strains t ij and c ij due to positive and negative stresses: 1 1 1 , 1 t t c c ij ijkl kl ij ijkl kl d C d C (10) 3 3 2 2 1 1 , t c i i i i t c i i (11) Note that in these expressions, strains labeled with a single indicia are principal strains. In uniaxial tension 1 t and 0 c . In uniaxial compression 1 c and 0 t . Hence, t d and t d can be obtained separately from uniaxial tests. The evolution of damage is provided in an integrated form, as a function of the variable : 0 0 1 1 exp t t t t A A d B (12) 0 0 1 1 exp c c c c A A d B . (13) Figure 1 . Evolution of two parts of damage t d and c d [5]. A direct tensile test or three point bend test can provide the parameters which are related to damage in tension ( 0 , t A , t B ). Note that Eq. 7 provides a first approximation of the initial threshold of damage, and the tensile strength of the material can be deduced from the compressive strength according to standard code formulas. The parameters ( c A , c B ) are fitted from the response of the material to uniaxial compression.

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