Issue 35

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.