Dynamic Behavior of Concrete: Constitutive Models - Dynamic Behavior of Concrete and Seismic Engineering - page 64

V 1

c

b

(K/2G + 2/3)Y 0

K

Y 0

a

2/3 Y 0

H 1

E

Figure 2.7. Axial stress-axial strain relationship: a) uniaxial stress state (simple
compression; b) isotropic or hydrostatic state; c) uniaxial strain state (oedometric)

Beyond the elasticity threshold, we can see that the uniaxial strain behavior
curve is parallel to the hydrostatic strain state behavior. By extrapolation, it is often
admitted that the behavior obtained in a uniaxial strain state, apart from the elasticity
threshold, is identical to the relationship between the pressure and the volume
variation in a hydrostatic case. However, we must not forget that this result relies on
such hypotheses as the von Mises criterion and plastic strain incompressibility.

Moreover, we can note the velocity of an “elastic” wave:

4
3

K G

c [2.9]

e

U

This conventional chain of reasoning can be extended to a Drucker Prager (or
Mohr Coulomb) criterion, which is more realistic with a material such as concrete.
The conclusions will then be different. The plasticity criterion is written the
following way:

VV AB VV [2.10]

1 2 1 2

Under oedometric loading, the plastification threshold (HEL) appears for the
stress level as: