Dynamic Behavior of Concrete: Experimental Aspects - Dynamic Behavior of Concrete and Seismic Engineering - page 39

Figure 1.19. Visco-elasto-plastic model with viscous strain hardening [SER 98a]. In this
1D diagram, the total strain H is the sum of the 3 scalar terms

H , x and H

Figure 1.20. Visco-elasto-plastic model with viscous strain hardening [SER 98a].
The plasticity criterion is translated into viscous strain hardening

Note that such modeling is below the localization of strains integrated into the
local description of the behavior. For the purpose of the study behind the
development of the model [TOU 99b], this limit seemed acceptable because
calculating the structure was not supposed to reveal any fracturing, and the
calculated strain rates appeared to be limited to about 1 s -1 .

For justifications based on “ultimate limit state” calculations including possible
localization of strains in part of the structure, the question of integrating inertial
effects into the local behavior description can be raised [MAL 98]. We have to be
aware of the theoretical difficulties caused by taking non-linearities into account,