PSI - Issue 33

Umberto De Maio et al. / Procedia Structural Integrity 33 (2021) 954–965 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

957

4

element mesh without requiring any remeshing techniques (see Fig. 1a). It is based on a variational formulation, detailly explained in (De Maio et al., 2020c), written for a spatially discretized domain subjected to body and surface forces as well as a prescribed displacement system.

Fig. 1. Schematic representation of the Diffuse Interface Model: (a) employed cohesive/volumetric finite element mesh; and (b) the adopted mixed-mode traction-separation law for the interface elements. The nonlinear constitutive behavior of the cohesive interfaces is expressed by a traction-separation law, reported in Fig. 1b, written in the following matrix form:

n         s   

(   = −   coh       coh 1 n s t t

0

  

0

K

)

(1)

d

n

0

0

K

s

The where d is a scalar damage variable with exponential evolution law that involves an effective displacement jump 2 2 m n s    = + , whereas, 0 n K , 0 s K and n  , s  are the normal/tangential components of the interfacial elastic stiffness K and the displacement jump u , respectively. The interfacial elastic stiffness playing the role of penalty parameter in order to enforce the inter-element kinematic constraint, without having a physical meaning. Correct values of these parameters ( 0 n K and 0 s K ) have been computed, adopting the micromechanics-based calibration technique proposed by some of the authors in (De Maio et al., 2020c), through the following expressions:

0 S n K E K K L   = = 0 0 , n

(2)

mesh

where E is the Young’s modulus of the material while  and  are dimensionless stiffness parameters obtained by the adopted calibration technique , as a function of the desired Young’s modulus reduction E R and the Poisson’s ratio of the bulk material. The mixed-mode initiation and propagation are governed by the following stress- and energy based criteria, respectively:

2

2

t

  

max       s    + t 

I G G G G Ic

n

(3)

1,

1

=

II + =



max

IIc