Issue 53

Z. Li et alii, Frattura ed Integrità Strutturale, 53 (2020) 446-456; DOI: 10.3221/IGF-ESIS.53.35

p

p

p







F

F

F

P

( , , )  σ D

=

+



+

=

σ

D

F

:

:

0

(33)

p

p









σ

D

p

D

D





F

F

D

=

=

( , ) Y D

: Y + D

(34)

F

:

0





Y

D

By drawing the constitutive equations, the plastic hardening law, and damage criterion (33)~(34), into one system, the plastic and damage multiplier can be determined [37-39]:

3 4 R R R R R R R R R R R R R R R R − − − − 2 6 1 5 2 6



1 6



= 

p

 

3 5

(35)

D  =  

2 4



3 5

where

s s

s s

2

p F

p

p

2

:  =      Y D , F Y  







Y







Y

F

ij ij

ij ij

e

= −



=

=

= −

σ

R

:

:

,

,

,

,

R

:

R

R

R

:

4

1

3

2

5

e

  D









  D



σ

Y

Y

2 6 J

6

J

D

p

D

p

D

2

D

2



:       Y







Y

F

=

: − 

.

R

6



Y     D D

D

Y





D

D

N UMERICAL SIMULATIONS

F

=

v =

or limestone, the below parameters are obtained in triaxial compression tests: 0 E

88.198

GPa

0.255

, 0

,

0.13  = ,

 =

 =

 =

m  =

 =

1.5 k = ,

m =

n =

B = −

r

0.004

m

1800

0.00012

0.00014

133

,

,

,

,

,

,

,

,

11.5

7.5

0.25

2

0

1

5

3  Pa. The dilute scheme, which is used for an elastic solid that has been weakened by an isotropic distribution of non-interacting closed microcracks[40-42], yields the following theoretical initial values of damage variable: 11 0.02 D = , 22 0.02 D = . 1.33  = , 0 4.9795 10 Y =

160

(σ 1 -σ 2 )/MPa

140

120

100

80

60

40

Present model

Experimental data ε 1 x10 -6

20

-6

ε

2 x10

0

-2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 3000 3500

Figure 2: Simulation of stress-strain curve under triaxial compressive test with confining pressure 10MPa

453