Scalar Damage Model for Cracking of Fixed Orientation

To convert the foregoing model into a damage model with unloading to the origin, it suffices to postulate that Cm and C-p are functions, not of the instantaneous value of £д, but of its maximum past value, defined as ifN. Thus, Cm and Op get “frozen" as soon as efN starts to decrease.

Although not strictly necessary, we may define a normal damage function similar to (8.4.4):

GCT

ШТ ~ 1 + GCT

 

U3N

 

and

 

(8.5.21)

 

from which (8.5.16) and (8.5.17) reduce to

1/(1 – Uljv) —V – V ~v 1 – V

—и —и 1

 

Gnn

G$s

Git

 

(8.5.22)

 

and

 

1 0

0 1/(1 – uT)

0 0

 

7ns

1st

Itn

 

G its Gst Gin

 

1

G

 

(8.5.23)

 

Scalar Damage Model for Cracking of Fixed Orientation

Scalar Damage Model for Cracking of Fixed Orientation

Подпись: - 2(1 f the model further simplifies,If we adopt the simple form (8.5.20) and select Ct because then

Scalar Damage Model for Cracking of Fixed Orientation

(8.5.24)

 

where we noted that the expression is identical to that for (he uniaxial case (8.4.4). This is the simplest possible model with unloading to the origin that is based only on the information from the uniaxial test.