PSI - Issue 41

Andrea Pranno et al. / Procedia Structural Integrity 41 (2022) 618–630 Author name / Structural Integrity Procedia 00 (2019) 000–000

624

7

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( 1) i 

j

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ij 



.

(13)

3. Investigation of the damage effects on the static and dynamic response of RC structural elements An investigation of the static and dynamic behavior of a reinforced concrete beam was performed comparing the numerical results with the experimental ones described by (Hamad et al., 2015). Based on the combination of DIM and ETM models, a numerical model is proposed and implemented using the finite element software COMSOL Multiphysics® 5.6. The proposed approach incorporates nonlinear springs to simulate the bond-slip mechanism between steel reinforcement bars and concrete and diffuse interface elements to simulate the nucleation of diffuse fractures in reinforced concrete structures. The geometry configuration, the material parameters and the cohesive law parameters were reported in Fig. 2, Tab.1 and Tab.2, respectively. The beam is restrained at both ends by supports consisting of highly stiffened plates used to spread the stress from the constraint reactions and by linear elastic springs simulating the elastomeric pads whose stiffness is equal 1.1x107 N/m.

Fig. 2. Geometry configuration and boundary conditions of the four-point bending test investigated (all dimensions are expressed in mm)

Tab. 1: Material mechanical properties.

Young’s Modulus [GPa]

Compressive strenght [MPa]

Traction strenght [MPa]

Poisson’s ratio

Yield strength [MPa]

Material

Concrete

40.3 210 210

0.20 0.30 0.30

-

36.5

2.10

Plain Steel Ø6 Ribbed Steel Ø10

393.6

- -

- -

490

Tab. 2: Parameters of the proposed cohesive law.

Ic G [N/m]

IIc G [N/m]

max  [Mpa]

max  [Mpa]

0 n K [N/m 3 ]

0 s K [N/m 3 ]







1.3162e14 1.3162e14

2.1

4.2

150 1500 5 250 0.5

As numerical result of the proposed nonlinear model, the load-deflection curve during the loading process (blue curve) exhibits a typical trilinear behavior, in which two slope variations are markedly observed, coinciding with the beginning of the main fractures in concrete (point A) and the yielding of the tension reinforcing longitudinal bars