PSI - Issue 82

Victor Rizov et al. / Procedia Structural Integrity 82 (2026) 253–259 V. Rizov/ Structural Integrity Procedia 00 (2026) 000–000

257 5

!

!

% " $#"! ! ! "

where

is the strain energy in the column.

is found integrating the strain energy densities,

,

% " $#"! ! ! "

% $ "#"! ! ! "

and

, in the layers of the column. Formulas (19), (20) and (21) are used for determining of the

strain energy densities.

"

!

! "$!#

& " ! # # & ! ! # # !

"

=

,

(19)

% ! "$!# # #

!

!

$ !#!"

"

=

,

(20)

% $ !#!" # #

!

!

!

! $#!"

& ! ! # #

"

=

.

(21)

% ! $#!" # #

!

The SERR yielded by (18) confirms the results found by (8). 3. Numerical results

"#!"" = !

!#!"! = !

"#!"" $ = !

"#!"" $ = !

!#!"! " = !

The SERR is analyzed for

m,

m,

m,

m,

,

m, . The results of this analysis are reported in the figures shown here. The SERR is presented as a function of the subsidence of the column in order to evaluate the effect of the subsidence magnitude on the delamination fracture behaviour. The corresponding curve is plotted in Fig. 3. The SERR in Fig. 3 is expressed in non-dimensional form. The increase of the subsidence magnitude causes a rapid growth of the SERR (Fig. 3). !#!"! " = ! !#!!" $ = ! " #"! = ! #"! = ! #"! = ! m, , and

Fig. 3. The SERR – subsidence curve.

Since the column has vscoelastic behaviour under constant strain, it is interesting to see the effect of relaxation of stresses on the delamination fracture. For this purpose, the SERR is obtained as a function of time. The diagram of this function is presented in Fig. 4. The continuous reduction of the SERR with time is a consequence of the relaxation behaviour. Since the parameters of the stress-strain-time constitutive laws of the column layers are distributed continuously