Dynamic Behavior of Concrete: Constitutive Models - Dynamic Behavior of Concrete and Seismic Engineering - page 84

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3 J q I 2

2 2 1

VV [2.50]

F ,, f 2 q f cosh 1 q f

¨ ¸

m 1 3

2

2 V

V

© ¹ m

m

The coefficients q and f characterize the material.

Coupling results from the fact that the damage scalar variable is linked to
porosity. At the initial state, the damage variable is not equal to zero, and can
decrease in the event of compaction.

Figure 2.20. Representation of Gurson's criterion in the plane
of the first two invariants (from [BUR 97])

2.6.6. Model deriving from a hydrodynamic approach

2.6.6.1. “ARMOR”

- Reference: [MAR 94].

- Principle: spherical and deviatoric separation of parts, perfect plasticity and
damage.

- Application field: concretes and rocks under high pressure.

- Can model: compaction.

- Cannot model: negative strain hardening.

- Model data:

i) the volume mechanism is represented by a relationship between pressure and
volume variation: