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Documentation

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: The meshes used in this project were created in SimScale with the standard algorithm. Manual refinements are used to control the cell sizes.

CaseElement TypeNumber of
Nodes
Element Technology
A1st Order Tetrahedral10435Standard
B2nd Order Tetrahedral70001Reduced Integration
Table 2: Mesh details for each case.

Find below the mesh used for case B. It’s a standard mesh with second-order tetrahedral cells.

hexahedral mesh for dynamic elastoplastic impact validation case
Figure 2: Finite elements mesh as used on case B

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
AJDX0.002890.00387-25.4%
ALDZ-0.01250-0.01346-7.1%
BJDX0.003650.00387-5.8%
BLDZ-0.01265-0.01346-6.0%
Table 3: Results comparison and computed error.

An 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

References

Note

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

Last updated: September 30th, 2021

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