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:
Point
X [m]
Y [m]
Z [m]
A
0
0
0
B
0.016
0
0
C
0.016
0.016
0
D
0
0.016
0
E
0
0
0.001
F
0.016
0
0.001
G
0.016
0.016
0.001
H
0
0.016
0.001
I
0
0
0.00327
J
0.0032
0
0.00327
K
0
0.0032
0.00327
L
0
0
0.03567
M
0.0032
0
0.03567
N
0
0.0032
0.03567
Table 1: Coordinates of the geometry vertices.
Analysis Type and Mesh
Tool Type: Code Aster
Analysis Type: Dynamic
Mesh and Element Types:
Case
Mesh Type
Number of Nodes
Number of Prisms
Number of Hexahedrals
Element Type
A
1st order prisms and hexahedrals
764
120
481
Standard
B
2nd order prisms and hexahedral
2861
120
481
Reduced Integration
C
2nd order prisms and hexahedrals
2861
120
481
Standard
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.
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 \( MPa \)
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 \( t = 9×10^{-5}\ s \):
CASE
POINT
COMP
COMPUTED
REF
ERROR
A
J
DX
0.00117536
0.00387
-69.6 %
A
L
DZ
-0.0134496
-0.01346
0.1 %
B
J
DX
0.00301416
0.00387
-22.1 %
B
L
DZ
-0.0126052
-0.01346
6.4 %
C
J
DX
0.00273561
0.00387
-29.3 %
C
L
DZ
-0.0125145
-0.01346
7.0 %
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:
Figure 4: Deformed shape with stress plot at t = 9e-5 s from case B.
Results by Stainier et al. as mentioned in [SDNV103]: L. Stainier and J.Ph. Ponthot. An improved one-point integration method for large strain elastoplastic analysis. Computer Methods in Applied Mechanics and Engineering, 118(1–2):163 – 177, 1994
Note
If you still encounter problems validating you simulation, then please post the issue on our forum or contact us.
Last updated: October 8th, 2020
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