PSI - Issue 39

Andrea Pranno et al. / Procedia Structural Integrity 39 (2022) 688–699 Author name / Structural Integrity Procedia 00 (2019) 000–000

691

4

  

  

n       s t t

n       s  

0

0

K





  

)[ ] K 0

(   1

   1

t

d

d

n

(1)

,

0

0

K

s

where    represents the displacement jump between the two crack faces, K 0 is the second-order constitutive tensor, d denotes a scalar damage variable, and the subscripts n and s denote the normal and the tangential components, respectively. The scalar damage variable d involves the following effective displacement jump:

2

2 ,

(2)





  

m

n

s

where  denotes the positive part of the enclosed quantity.

Fig. 1. Schematic representation of the DIM approach.

In this work the normal and tangential stiffness parameters n K 0 and s K

0 are defined by the following relation:

E

   0 0

(3)

,

K K

n

S

L

mesh

where E is the Young’s modulus of the concrete, mesh L denotes the average mesh size, and   200 represents a dimensionless stiffness parameter. Such assumptions were assumed according to the micromechanical approach proposed by some of the authors in De Maio et al. (2020d). In Figure 2 the proposed trilinear traction-separation for nano reinforced UHPFRC is reported. It is based on a trilinear softening model proposed by Park et al. (2010) for functionally graded materials and it is able to capture micro-cracking phenomena of the cement paste, debonding phenomena in the matrix/aggregate interfaces, and fiber pull-out. In addition, the proposed cohesive law is also able to take into account the increase of the fracture resistance