Dynamic Behavior of Concrete: Constitutive Models - Dynamic Behavior of Concrete and Seismic Engineering - page 71

- plasticity or viscoplasticity theory, which describes sliding and shear;
- pressure-volume relationships or hydrodynamic state laws for compaction.
Figure 2.15. Diagram of the elastic domain for concrete and of the different irreversible
phenomena in the plane of the first two invariants of the stress tensor
2.5.2. Integrating sensitivity to the strain rate
2.5.2.1. Models with time dependence
If we want to integrate the observed sensitivity to strain rate into the behavior
model, the latter can intervene within the framework of conventional models.
Linear or non-linear visco-elasticity will reveal an apparent stiffness increase
with the strain rate. If failure modeling is of the perfect brittle type and if the failure
criterion is expressed as maximum strain, we will find that strength increases with
the strain rate.
Visco-plasticity will show up as an apparent strength increase, in terms of the
maximum stress reached rising with the strain rate.
Rate effects can also be introduced within the evolution of damage.
It is necessary to justify the introduction of the dependence on rate. Two reasons
justify the use such a process:
- a physical argument, because we wish to use the model to describe a real event
that has been observed experimentally. We must refer to Chapter 1 and see how
cautiously these apparent dynamic strength increases must be interpreted;
- a theoretical argument, because dependence on rate within a viscoplastic or
“viscous-damage” framework allows us to preserve a well-posed structure
calculation problem, even in the presence of softening.