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Validation Case: Impact of an Elastoplastic Bar

This validation case belongs to an elastoplastic impact in solid mechanics. The aim of this test case is to validate the following parameters:

  • Dynamic analysis
  • Frictional contact
  • Elastoplasticity
  • Large deformations

The simulation results of SimScale were compared to the numerical results presented in [SDNV103]\(^1\).

Geometry

The geometry used for the case is as follows:

geometrical model for dynamic elastoplastic impact validation case
Figure 1: Geometrical model of the impact bar and plate.

It represents an elastoplastic bar in the z-direction and a rectangular plate in the x-y plane with the following coordinates for each point:

PointX [m]Y [m]Z [m]
A000
B0.01600
C0.0160.0160
D00.0160
E000.001
F0.01600.001
G0.0160.0160.001
H00.0160.001
I000.00327
J0.003200.00327
K00.00320.00327
L000.03567
M0.003200.03567
N00.00320.03567
Table 1: Coordinates of the geometry vertices.

Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Dynamic

Mesh and Element Types:

CaseMesh TypeNumber of
Nodes
Number of
Prisms
Number of
Hexahedrals
Element Type
A1st order prisms
and hexahedrals
764120481Standard
B2nd order prisms
and hexahedral
2861120481Reduced Integration
C2nd order prisms
and hexahedrals
2861120481Standard
Table 2: Mesh details for each case.

The tetrahedral mesh was computed using SimScale’s Standard mesh algorithm and manual sizing. The hexahedral meshes were computed locally and uploaded into the simulation project.

hexahedral mesh for dynamic elastoplastic impact validation case
Figure 2: Finite elements mesh as used on cases A, B and C.

Simulation Setup

Material:

  • Bi-linear Plasticity Isotropic:
    • \( E = \) 117 \( GPa \)
    • \( \nu = \) 0.35
    • \( \sigma_y = \) 400 \( MPa \)
    • \( E_T = \) 500 \( MPa \)
material elastoplastic model for dynamic elastoplastic impact validation case
Figure 3: Material elasto-plastic stress-strain curve.

Boundary Conditions:

  • Initial Conditions:
    • Velocity of 227 \(m/s \) to volume IJKLM (bar)
  • Constraints:
    • Volume ABCDEFGH (plate) fixed
    • Face IKLN zero x-displacement
    • Face IJLM zero y-displacement

Reference Solution

The reference solution is from a numerical computation as presented section 2 of [SDNV103]\(^1\), which are taken as the mean results of [Stainer]\(^2\):

\( DX_J = 3.87 mm \)

\( DZ_L = 13.46 mm \)

Result Comparison

Comparison of displacements at points J (DX) and L (DZ) at time \( t = 9×10^{-5}\ s \):

CASEPOINTCOMPCOMPUTEDREFERROR
AJDX0.001175360.00387-69.6 %
ALDZ-0.0134496-0.013460.1 %
BJDX0.003014160.00387-22.1 %
BLDZ-0.0126052-0.013466.4 %
CJDX0.002735610.00387-29.3 %
CLDZ-0.0125145-0.013467.0 %
Table 3: Results comparison and computed error.

Illustration of the final shape (case B) can be found in Figure 4. The elastoplastic deformation due to the impact can be appreciated:

results plot for dynamic elastoplastic impact validation case
Figure 4: Deformed shape with stress plot at t = 9e-5 s from case B.

Tutorial: Crash Test of FSAE Impact Attenuator

References

Note

If you still encounter problems validating you simulation, then please post the issue on our forum or contact us.

Last updated: July 13th, 2020

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