11.3 Analytical Methods for Predicting the Dynamic Responses …
379
Table 11.3 Material parameters for steel tube, steel support and UHPCC
Material
Parameter
Value
Steel
tube (*MAT_PIECEWISE_LINEAR_PLASTICITY)
Density
7750 kg/m 3
Young’s
modulus
206 GPa
Poisson’s ratio 0.3
Yield stress
318.5 MPa
Strain rate
parameter C
6844 s −1 (Li et al.
2018)
Strain rate
parameter P
3.91 (Li et al. 2018)
Steel support (*MAT_RIGID)
Density
7750 kg/m 3
Young’s
modulus
206 GPa
Poisson’s ratio 0.3
UHPCC (*MAT_CONCRETE_DAMAGE_ REL3)
Density
2480 kg/m 3
Poisson’s ratio 0.23
Compressive
strength
141.5 MPa
1E-6 1E-5 1E-4 0.001 0.01 0.1
1
10 100 1000
0.5
1.0
1.5
2.0
2.5
DIF for compressive strength
Ren et al. 2018b
Eq. (10.2)
Strain rate (s
-1
)
1E-7 1E-6 1E-5 1E-4 0.001 0.01 0.1 1 10 100 1000
0
2
4
6
8
10
12
14
16
DIF for dynamic tensile strength
Wu et al. 2018b
Eq. (10.3)
Strain rate (s
-1
)
(a)
(b)
Fig. 11.7 Empirical DIF relations for UHPCC a compression b tension, reprinted from Wu et al.
(2020), copyright 2020, with permission from Elsevier
DIF
c
c =
(˙ ε/˙ ε 0 )
0.014
for ˙
ε ≤ 62s
−1
0.587(log˙ ε)
2
− 1.435log˙ ε + 1.911 for ˙
ε > 62s
−1
(11.2)
DIF
t
c =
(˙ ε/˙ ε 0 )
0.018
for ˙
ε ≤ 10.3s
−1
9.959log˙ ε − 8.718 for ˙
ε > 10.3s
−1
(11.3)