8.5 Numerical Simulation
261
employed for modelling the steel tube, UHPCC, drop hammer, supporting frames as
well as the steel plate welded at the end of the column.
For the numerical simulation of the interface between the steel tube and core
concrete, by adding a slip element between a steel tube element and a core concrete
element, Hajjar (1998) and Bangash (1989) derived that, considering the slip property
between the interfaces has little influence on the dynamic behavior of CFST. Thus
the slip is not considered at present.
The interface between the steel tube and UHPCC were completely bonded
by using a common-node approach, which is consistent with the fact that
the steel tube and core concrete are tightly bonded. The contact between
the drop hammer and steel tube, as well as the contact between the
steel tube and supporting frames, were described by using the keyword
“*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE” implemented in LSDYNA (LS-DYNA Keyword User’s Manual 2014), respectively. As for the two
deformable surfaces in contact, the master surface refers usually to the stiffer body
or the surface with a coarser mesh if the two surfaces have comparable stiffness
(LS-DYNA Keyword User’s Manual, 2014). Therefore, the FE procedure selects the
supporting frame as the master surface in contact with the steel tube (slave surface),
and defines the steel tube as the slave surface in contact with the drop hammer (master
surface).
8.5.1.2 Steel Tube Material Model
The Cowper-Symonds (CS) model (1957) and Johnson–Cook (JC) model
(1983) are the common constitutive models for steel material. JC model
(*MAT_JOHNSON_COOK in LS-DYNA (LS-DYNA Keyword User’s Manual
2014)) is specially developed for materials subjected to large strain, high
strain rate and high temperature, it is less popular than the former one
in modeling the behavior of steel under low-velocity impact. Therefore, CS
model (*MAT_PLASTIC_KINEMATIC in LS-DYNA (LS-DYNA Keyword User’s
Manual 2014)) with linear isotropic hardening and strain rate effect is adopted in the
simulation, which has the reputation of minimizing the duration of analysis.
In CS model, the yield stress scaled by a strain rate dependent factor is expressed
by:
σ d
σ s
= 1 +
˙
ε
C c
1/P c
(8.24)
where σ d and σ s denote the dynamic flow stress and the associated static flow stress,
respectively. ˙
ε represents the strain rate. C c and P c are the strain rate parameters, and
the values of 40 and 5 are adopted according to the findings in Stouffer and Dame
(1996). Table 8.10 lists the material parameters of CS model for the steel tube, in
which the tangent modulus E t is obtained by using the following equation.
261
employed for modelling the steel tube, UHPCC, drop hammer, supporting frames as
well as the steel plate welded at the end of the column.
For the numerical simulation of the interface between the steel tube and core
concrete, by adding a slip element between a steel tube element and a core concrete
element, Hajjar (1998) and Bangash (1989) derived that, considering the slip property
between the interfaces has little influence on the dynamic behavior of CFST. Thus
the slip is not considered at present.
The interface between the steel tube and UHPCC were completely bonded
by using a common-node approach, which is consistent with the fact that
the steel tube and core concrete are tightly bonded. The contact between
the drop hammer and steel tube, as well as the contact between the
steel tube and supporting frames, were described by using the keyword
“*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE” implemented in LSDYNA (LS-DYNA Keyword User’s Manual 2014), respectively. As for the two
deformable surfaces in contact, the master surface refers usually to the stiffer body
or the surface with a coarser mesh if the two surfaces have comparable stiffness
(LS-DYNA Keyword User’s Manual, 2014). Therefore, the FE procedure selects the
supporting frame as the master surface in contact with the steel tube (slave surface),
and defines the steel tube as the slave surface in contact with the drop hammer (master
surface).
8.5.1.2 Steel Tube Material Model
The Cowper-Symonds (CS) model (1957) and Johnson–Cook (JC) model
(1983) are the common constitutive models for steel material. JC model
(*MAT_JOHNSON_COOK in LS-DYNA (LS-DYNA Keyword User’s Manual
2014)) is specially developed for materials subjected to large strain, high
strain rate and high temperature, it is less popular than the former one
in modeling the behavior of steel under low-velocity impact. Therefore, CS
model (*MAT_PLASTIC_KINEMATIC in LS-DYNA (LS-DYNA Keyword User’s
Manual 2014)) with linear isotropic hardening and strain rate effect is adopted in the
simulation, which has the reputation of minimizing the duration of analysis.
In CS model, the yield stress scaled by a strain rate dependent factor is expressed
by:
σ d
σ s
= 1 +
˙
ε
C c
1/P c
(8.24)
where σ d and σ s denote the dynamic flow stress and the associated static flow stress,
respectively. ˙
ε represents the strain rate. C c and P c are the strain rate parameters, and
the values of 40 and 5 are adopted according to the findings in Stouffer and Dame
(1996). Table 8.10 lists the material parameters of CS model for the steel tube, in
which the tangent modulus E t is obtained by using the following equation.