RDE: 0300 SBeam Crash
An Sbeam is crushed against a rigid wall with initial velocity.
 Shell element formulations
 BATOZ: I_{shell}=12
 QEPH: I_{shell}=24
 Q4 Belytschko: I_{shell}=3
 Global integration versus 5 integration points in shell element
 Influence of the initial velocity (5 m/s and 10 m/s)
 Deformation configuration
 Crushing force
 Computation cost
 Kinetic energy
 Internal energy
Options and Keywords Used
 Selfimpacting contact (/INTER/TYPE7)
 Elastoplastic material (/MAT/LAW2 (PLAS_JOHNS))
 Initial velocities (/IMPVEL)
 Rigid body (/RBODY)
 Shell section properties (/PROP/TYPE1 (SHELL), I_{shell}) (element formulation), N (Integration points)
Input Files
Model Description
An Sbeam is crushed at an initial rate of 5 m/s against a rigid wall. The section is an empty squareshaped tube (each side measuring 80 mm).
The mesh is a regular shell mesh. Each shell element measures approximately 5 mm x 5 mm.
The following system is used: mm, ms, g, N, MPa
 Material Properties
 Value
 Young's modulus
 199355 $\left[\mathrm{MPa}\right]$
 Poisson's ratio
 0.3
 Density
 7.9x10^{3} $\left[\frac{g}{m{m}^{3}}\right]$
 Yield stress
 185.4 $\left[\mathrm{MPa}\right]$
 Hardening parameter
 540 $\left[\mathrm{MPa}\right]$
 Hardening exponent
 0.32
 Maximum stress
 336.6 $\left[\mathrm{MPa}\right]$
Simulation Iterations
 Shell element formulations:
 BATOZ: I_{shell}=12 fullyintegrated shell element, no hourglassing
 QEPH: I_{shell}=24 Reduced integration element with physical hourglass stabilization
 Q4 Belytschko: I_{shell}=3 Reduced integration element with elastoplastic hourglass with orthogonality
 Through thickness integration method:
 Global integration (N=0)
 5 integration points (N=5)
 Influence of the initial velocity:
 5 m/s and 10 m/s
Two rigid bodies were created at the left and right side. Boundary conditions, velocity and added mass are applied on the rigid bodies.
 Fixed in the Z translation, and x, y, z rotation
 Initial velocity of 5 m/s in the X direction
 A 500 Kg mass is added on the left end to the rigid body
Results
Influence of Different Shell Formulation with N=5
Influence of Different Integration Points
1 CPU [normalized] 
Maximum Plastic Strain  

BT TYPE3 (I_{shell}=3) 
N=0  0.41  0.981 
N=3  0.56  1.596  
N=5  0.73  1.605  
BATOZ (I_{shell}=12) 
N=0  1.78  1.054 
N=3  2.53  1.471  
N=5  3.24  1.486  
QEPH (I_{shell}=24) 
N=0  0.65  0.958 
N=3  0.78  1.516  
N=5  1.00  1.586 
Initial Velocity Influence
Figure 8 show the influence of the crushing velocity (5 m/s and 10 m/s). This example uses the QEPH shell formulation (I_{shell}=24) with 5 integration points (N=5).
Internal Energy
IE [mJ] 
Kinematic Energy
[mJ] 


V=5 m/s  1.674E+6 (factor 1.0) 
4.574E+6 (factor 1.0) 
V=10 m/s  4.443E+6 (factor 2.654) 
2.056E+7 (factor 4.495) 
Conclusion
The BATOZ (I_{shell}=12) and QEPH (I_{shell}=24) element formulations provide accurate results. Although the Q4 Belytschko (I_{shell}=3) element is faster, there is always the possibility of hourglassing as shown in RDE: 0100 Twisted Beam. Although more expensive than the Q4 Belytschko element, the QEPH element does not have the hourglassing issue and provides results that are very similar to the more expensive fullyintegrated BATOZ element.
Using global integration (N=0) is faster but not as accurate as using N=5 integration points. The global integration results show an underestimation of the plastic strain and can only be used with a limited number of material laws.