PSI - Issue 41

Andrea Pranno et al. / Procedia Structural Integrity 41 (2022) 618–630 Author name / Structural Integrity Procedia 00 (2019) 000–000

622

5

0 n K denoting the initial stiffness under tensile and compression stresses.

with

Fig. 1. Proposed traction-separation law for loading and unloading tensile cycle written in terms of normal displacement jump.

The following relations define the proposed cohesive law when the normal cohesive stresses swap from tension to compression:   0 0 0 c p p p n n n n n n compression n p n n n n K t K                  , (5)

p c n n K K K   c

p   

,

(6)

0

n

0

n

n

 1  

   

0

p

K

K

n

n

c

K



,

(7)

n

1



with  representing a scalar factor which allow to reduce the initial compression stiffness 0 n K as the level of damage increases to simulate the partial contact between the cracks surfaces due to the presence of aggregates. A quadratic nominal stress criterion governs the crack initiation:

2

2

t

  

    

  

t

n

1



s

,

(8)









max

max