Models for Simulating the Seismic Response of Concrete Structures - Dynamic Behavior of Concrete and Seismic Engineering - page 246

giving correct results [ILE 00]. This parameter can be adjusted. Whenever there is a
pronounced rotation of the main directions, a second series of cracks is created
perpendicular to the existing one.

7.3.3.3. Cyclic uniaxial law

The uniaxial law implemented allows us to account for the main phenomena
observed when loading consists of a few alternating cycles.

Stress

PF

f c

E 0

f t

2

1

E ts

8 3

H tm

7 Strain

9

E 1

4

E 1

-f t

E 2

6

5

-f c

Figure 7.10. Response of the model to a traction-compression cycle

Let us examine (Figure 7.10) the behavior of a point initially in traction which
cracks completely before being subjected to opposite compression reloading. The
concrete is elastic until the strength in simple traction is reached: f t (path 1), then it
cracks according to negative stiffness (slope E ts , path 2), up to a H tm

H strain.
Beyond this, crack opening occurs without any stress (path 3). When the stress
changes its direction, an increasing compression stress is necessary for the crack to
gradually close up (slope E 1 z E 0 , path 4). The latter is considered to be completely
closed for a stress lower than -f t , the value at which stiffness is completely restored
(path 5). The description of path 4 is based on tests that show the opposite lips of a
crack do not coincide, that they become strained under the effect of a stress which
tends to close the crack up, and that the stiffness of the uncracked concrete is only
restored with complete closing. Nevertheless, the crack closes up with a stress equal

trac
rupture