Issue 39

M. A. Lepore et alii, Frattura ed Integrità Strutturale, 39 (2017) 191-201; DOI: 10.3221/IGF-ESIS.39.19 195   n n n n n n D K K 0 0 1 ,   0 ,   0             (6)   s s D K 0 1     (7) where D is the damage function and the initial stiffness K n0 and K s0 are the slope of the first segment of mode I and mode II cohesive curve, respectively. The structure of the algorithm requires the displacement jump u and its relative increments d u as data input, whilst provides as output with  ,  and its derivative respect to the displacement jump components. For each integration step, the value of displacement jump across the interface  n is compared with the state variable  max , which is associated with the current damage (5), reported here:       max t 0,  max       where t is the variable time. When separation is greater than previous  max , i.e. the point (  curr ,  curr ) is located on the effective limit curve   n f    (Fig. 4), the damage D is increasing according to the relationship ncurr n KD K 0 1   (8) Being curr  equal to the updated max  , the current stiffness is   max ncurr n max f K       (9) whilst the initial stiffness   n K f 0 0   (10) Then, the stress field is recalculated according to Eqs. (6)-(7).   n   max ( t )   curr ( t )  f (  curr )  K curr  P 1  P 2  P i  P n  Figure 4 : Interpolated cohesive law – opening of the interface.