Dynamic Behavior of Concrete: Experimental Aspects - Dynamic Behavior of Concrete and Seismic Engineering - page 38

For more comprehensive calculations, strength evolution is insufficient, as the
strain speed value is not constant and cannot define the behavior characteristics
alone. In addition, strain data during characterization experiments (modulus, limit
strains) are not abundant and are sometimes contradictory because of difficulties
with measurements and interpretations (like localization, the effects of which have
been described when mobilizing inner inertial loads), as shown by [COL 88], [BIS
91] and [SER 98a].
A “unified” use of results published in the literature can lead to a description of
the dynamic behavior of the material through the “evolution” of its static behavior.
The advantage of this approach is that it covers a priori (using a conventional three-
dimensional interpretation) all possible stress states, whilst also taking advantage of
the (rather rare) validations of criteria in strongly tri-axial stress domains. However,
from this perspective, using viscoplasticity or damage models with “standard”
gradients has limitations, because experimental data coincide rather badly with the
calibration of viscosity aimed at mastering numerical regularity problems ([GEO
98], [TOU 95b]).
This is why it has been necessary to explore more complex modeling by
extension of a damageable elasto-plastic model, thanks to a strain-hardening
variable with the same nature as a viscous strain [SER 98B]. This inner variable
corresponds to an extension strain (Figure 1.19), in so far as the rate effects are
principally linked to the deviatoric component of the stress state, the intervention of
confinement delaying localization of failure in the potential growth direction, the
same as in statics [KON 01]. The methodology for identifying the parameters of the
model from a relatively low number of well controlled empirical data points (direct
traction tests at various rates) have been detailed and validated by traction
simulations, compression and shear tests on specimens, and bending tests on slabs
[SER 98b]. These simulations have allowed it to be validated within the studied
domain, for testing hypotheses about the kinematic nature of viscous strain
hardening (Figure 1.20). The validation of such an approach should be continued
using high-confinement tests ([GON 90], [GRA 89], [MAL 91]). As for the problem
of falling containers, which was used as a basis for this development, the importance
of the various sophistications of the model (damaging, taking viscous strain-
hardening into account) was verified by a sensitivity study, which essentially
showed the behavior of the studied structure was governed by both local
compression of concrete at the impact point and propagation of induced tractions
within part of the structure where confinement was weak [SER 98a].