8. Keyword factor ENDO_LOCA_EXP

Behavior model ENDO_LOCA_EXP is a local damagable elastic behavior model. It makes it possible to describe the softening behavior of concrete. In particular, it distinguishes between tensile and compressive behavior, partially restores compressive stiffness and describes shear or bi-traction states well. Because of its local character, it is dedicated to a homogenized representation of structural cracks, which explains the introduction of an inter-crack distance that fixes the size of the areas containing at most one crack. At the scale of this zone, his response is close to that of ENDO_FISS_EXP, which would describe the detail of the crack. Some parameters are therefore common with those in ENDO_FISS_EXP. For more information, please refer to document [R7.01.42] and the references cited there.

8.1. Operands

E	Young’s modulus (Pa)
NU	Poisson’s ratio
FT	Single Tensile Strength (Pa)
FC	Simple Compressive Strength (Pa)
GF	Cracking energy (N/m)
P	Work hardening parameter
DIST_FISSURE	Average inter-crack distance (m)
REST_RIGI_FC	Stiffness restoration coefficient (0 = without restoration)

Table 8.1-a: Material parameters of law ENDO_LOCA_EXP

8.2. How it works

Some characteristics do not require additional explanations: Young’s modulus, Poisson’s ratio, tensile and compressive strengths, and cracking energy. These are common characteristics for modeling concrete damage.

The parameter P influences the shape of the work hardening, leading to a stress-deformation response that is all the more curved the greater it is. It is analogous to the parameter Pde in law ENDO_FISS_EXP. There is no other parameter characterizing work hardening: compared to ENDO_FISS_EXP, we chose to take Q=0.

As far as stiffness restoration is concerned, model ENDO_LOCA_EXP introduces a regulation parameter \(\gamma\) which smoothes the stiffness jump between traction and compression. Rather than directly entering the value of \(\gamma\), which is not necessarily very meaningful, we prefer to indicate via REST_RIGI_FC the level of stiffness restored with respect to the initial stiffness for a deformation (in compression) equal to FC/E. This value is therefore between 0 (no restoration of rigidity) and 1 (strictly less than 1, the total restoration of stiffness not being possible with the chosen regularization function). A value of 0.95 is proposed by default.

Finally, DIST_FISSURE introduces the average inter-crack distance, which depends in particular on the reinforcements in the concrete. In practice, only the GF/ DIST_FISSURE ratio plays a role but it was preferred to keep the two parameters because each has a specific physical meaning. For reasons of local stability of the model (no snap-back at the scale of the hardware point), there is an upper bound to the inter-crack distance that can be modelled. Compliance with this condition is checked during data entry.