PSI - Issue 54

Victor Rizov et al. / Procedia Structural Integrity 54 (2024) 475–481 Victor Rizov/ Structural Integrity Procedia 00 (2019) 000 – 000

477 3

In expressions (1) and (2), l is the beam span, 2 l is the distance between point, 1 B , and the right-hand end of the beam (Fig. 1). The moment of bending, ct M , in the delamination-tip cross-section of the beam is obtained as t M ct     , (3) where l Fl a 1   , l Fv a F   .

Fig. 2. Non-linear viscoelastic model.

i E  , in the spring are related as:

 , and strain,

The model displayed in Fig. 2 is used here. The stress, i E

n i E E 

E  

,

(4)

i i

i

i E and i n are parameters, m is the number of layers. The stress, i   , and

m i 1, 2, ...,  . In formula (4),

where

i   , in the dashpot of the model are related as   i i i p i        ,

the strain,

(5)

where i  and i p are model parameters. The strain, i  , in the viscoelastic model is determined as

 

    .

(6)

i

E

i

i

i  , that is a linear function of the time

The model (Fig. 2) is under stress,

t i    .

  0

(7)

i

i

Here, i  is the velocity. The stress,

i E  , is written as (Fig. 2)



  .

(8)

E i

i

From (4), (7) and (8), it follows that   i i i n i E t 1      ,

(9)



i 

i 0

 

 

where

,

. From Fig. 1, it is clear that

i

i

E

E

i

i

 

  .

(10)

i

i

Formulae (5) and (10) indicate that   i i i p i t 1        ,

(11)



i   i

0  ,

i 

 

. By integrating of (11), one obtains

where

i i 

i