Dynamic Behavior of Concrete: Constitutive Models - Dynamic Behavior of Concrete and Seismic Engineering - page 61

Figure 2.6. Triaxial compression tests on MB50 concrete. Strain-longitudinal stress diagrams
Figure 2.5 shows loading paths for concrete tri-axial tests. Figure 2.6 presents the
relationship between axial stress and axial strain. We can note the brittle-ductile
transition for a confinement pressure of about 50 MPa.
2.1.5.1. Strain rate ranges
Is it possible to establish a relationship between a dynamic loading and the strain
rate it would impose on the structure material? Generally not. The strain rate is
meaningful for a model describing the structure's movement. It is necessary to make
a difference between the scale of the structure and the local scale as they have been
defined above.
At the scale of the structure , the model describes a beam or a slab element under
bending, for instance. The model implies a specific time-scale - that of the period of
the bending mode taken into account. Thus, we implicitly admit that the propagation
time for a distance corresponding to the size of the element is much shorter. This
modeling scale is consistent for seismic calculations and for the overall effect of an
impact on a structure. Within that frame, the strain rates can reach the 1/s order of
magnitude.
On the local scale, we can observe the wave propagation in a continuum. The
strain rate can be quite high (10 to 1,000/s). The strain rate is a function of the strain
level (which depends on the loading) and the wave velocity (which depends on the