# RD-E: 0300 S-Beam Crash

An S-beam is crushed against a rigid wall with initial velocity.

A sensitive study is performed on an S-beam with a crushing load condition. This model uses an elasto-plastic Johnson-Cook material with a penalty based auto-impacting self-contact interface to model the buckling of the beam. An initial velocity is applied on the left section via a kinematic condition with a rigid body. The impacting condition is sliding and modeled using boundary conditions on the right section.
Three different parameters are varied and results compared:
• Shell element formulations
• BATOZ: Ishell=12
• QEPH: Ishell=24
• Q4 Belytschko: Ishell=3
• Global integration versus 5 integration points in shell element
• Influence of the initial velocity (5 m/s and 10 m/s)
The following criteria is used to compare results:
• Deformation configuration
• Crushing force
• Computation cost
• Kinetic energy
• Internal energy

## Input Files

Before you begin, copy the file(s) used in this example to your working directory.

## Model Description

An S-beam is crushed at an initial rate of 5 m/s against a rigid wall. The section is an empty square-shaped tube (each side measuring 80 mm).

The thickness is 1.5 mm. The tube is made of steel, and plasticity is considered, but not failure.

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

The material properties used for isotropic elasto-plastic Johnson-Cook law.
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

A sensitive study is performed comparing:
• Shell element formulations:
• BATOZ: Ishell=12 fully-integrated shell element, no hourglassing
• QEPH: Ishell=24 Reduced integration element with physical hourglass stabilization
• Q4 Belytschko: Ishell=3 Reduced integration element with elasto-plastic 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.

The left section undergoes the following conditions:
• 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

The different shell element formulation only slightly changes the crushing force. The plastic strain results are also similar for these three shell element formulations. Looking at computational cost, the QEPH element is 3 times faster than the fully-integrated BATOZ element. The Q4 TYPE3 Belytschko element is 1/3 times faster than the QEPH, but the Q4 BT TYPE3 element is more susceptible to hourglassing, so QEPH is normally recommended.

### Influence of Different Integration Points

Table 1 shows that the maximum plastic strain for all elements with global integration (N=0) returns results too low when compared to 5 integration points through the thickness (N=5). When calculating material plasticity through the thickness, using more integration points will increase the accuracy but is computationally more expensive. In general, N=5 is considered a good compromise between computational speed and accuracy. Although using global integration may speed up the computation, it is only compatible with Material Laws 1, 2, 22, 36, 43 and 60 and cannot be used with the failure models (/FAIL) . For additional information, refer to the FAQ Materials/Failure.
Table 1. Computation Cost for Global Integration (N=0), N=3, and N=5
1 CPU

[normalized]

Maximum Plastic Strain
BT TYPE3

(Ishell=3)

N=0 0.41 0.981
N=3 0.56 1.596
N=5 0.73 1.605
BATOZ

(Ishell=12)

N=0 1.78 1.054
N=3 2.53 1.471
N=5 3.24 1.486
QEPH

(Ishell=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 (Ishell=24) with 5 integration points (N=5).

The higher initial velocity gives a larger initial kinematic energy which leads to more deformation and absorbed energy in the beam.
Table 2. Energy for the Different Velocities
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 (Ishell=12) and QEPH (Ishell=24) element formulations provide accurate results. Although the Q4 Belytschko (Ishell=3) element is faster, there is always the possibility of hourglassing as shown in RD-E: 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 fully-integrated 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 under-estimation of the plastic strain and can only be used with a limited number of material laws.