Dynamic Behavior of Concrete: Constitutive Models - Dynamic Behavior of Concrete and Seismic Engineering - page 63

If the plasticity criterion is of the Tresca or von Mises type:

VV

Y

[2.5]

1 2

In the elastic phase the relationships between stresses and strains are as follows:

Ev 1

4

VOPH 2 H KG H

1 1 1 1

3

12 1 v v

and [2.6]

v

V V

2 1

1 v

At the plasticity threshold:

§ v · 1 v § K 2 ·

VV 1 V Y and V Y Y [2.7]

¨ ¸ ¨ ¸

1 2 1 0 1 0 0

1 v 12 v 2 G 3

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This elastic limit in a uniaxial strain state is also called Hugoniot's elastic limit
(HEL). Beyond the flow threshold:

2
3

VH K Y [2.8]

1 1 0

The observable behavior is shown in Figure 2.7, together with the hydrostatic
strain behavior and the uniaxial strain state behavior (simple compression).