5. D modeling#
5.1. Characteristics of modeling#
This is an elasto-plasticity calculation under the hypothesis of small displacements, with the X- FEM method (non-meshed crack). We represent the opening of the crack and its closure by activating the contact on the lips.
Compared to modeling C, non-linear elasticity is replaced by elasto-plasticity. Up to time 0.1, the loading is monotonic and the results are therefore identical between the models C and D. In the modeling D, a discharge is then carried out and an opposite loading is applied, thus activating the contact on the lips of the crack.
5.2. Characteristics of the mesh#
The mesh is identical to that of the C modeling.
5.3. Tested sizes and results#
Two quantities are tested:
the \(\mathrm{DY}\) component of the displacement at the two points where the crack opens (points on each of the lips), at the instant 0.1 of the calculation (imposed displacement \(\mathrm{0,1}\mathrm{mm}\)) and at the last moment 0.3 (imposed displacement \(-\mathrm{0,1}\mathrm{mm}\));
the values of the effective plastic deformation (\(\mathrm{V1}\)) on the \(\mathrm{M277}\) mesh, in the point 10 and at the times 0.1, 0.14 and 0.3.
For the moment 0.1, the reference value of the displacement is the solution obtained in modeling A. For the rest, the tests are non-regression.
Movement |
Reference ( \(\mathrm{mm}\) ) |
Aster_Code ( \(\mathrm{mm}\) ) |
Difference ( \(\text{\%}\) ) |
Lip \(y>0\), \(t=0.1\) |
9,876.10-2 |
9,532.10-2 |
-3.5% |
Lip \(y<0\), \(t=0.1\) |
-9,876.10-2 |
-9,533.10-2 |
-3.5% |
Lip \(y>0\), \(t=0.3\) |
1,782.10-2 |
Non-regression |
|
Lip \(y<0\), \(t=0.3\) |
-1,782.10-2 |
Non-regression |
|
Effective plastic deformation ( \(\mathrm{V1}\) on \(\mathrm{M277}\) ) |
|||
\(t=0.1\) |
1.270.10-2 |
Non-regression |
|
\(t=0.14\) |
1.270.10-2 |
Non-regression |
|
\(t=0.3\) |
2.451.10-2 |
Non-regression |
|
This test validates the elasto-plasticity calculation for X- FEM models.