1. Reference problem#
1.1. Geometry#
We consider a 1×1 mm square test piece comprising 4 elements.
Figure 1-1: Square of 4 elements in tension
1.2. Material properties#
We adopt a Von Mises elasto-plastic behavior law with isotropic work hardening TRACTION whose traction curve is given point by point:
\(\mathrm{\epsilon }\) |
0.0027 |
0.005 |
0.005 |
0.01 |
0.01 |
0.015 |
0.02 |
0.03 |
0.04 |
0.05 |
0.05 |
0.05 |
0.075 |
0.1 |
|
\(\mathrm{\sigma }\) \(\mathit{MPa}\) |
555 |
589 |
589 |
631 |
631 |
657 |
676 |
691 |
704 |
725 |
741 |
741 |
741 |
772 |
794 |
0.125 |
0.15 |
0.2 |
0.2 |
0.3 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.8 |
0.9 |
812 |
827 |
851 |
887 |
887 |
97 |
912 |
933 |
950 |
965 |
978 |
990 |
The deformations used in the behavior relationship are linearized deformations. Young’s modulus \(E\) is \(200\mathit{GPa}\) while the Poisson’s ratio \(\mathrm{\nu }\) is equal to \(\mathrm{0,3}\).
The Weibull model coefficients used are as follows:
\(m=8\),
\({V}_{0}=125\mathrm{\mu }m\),
\({\mathrm{\sigma }}_{u}=2630\mathit{MPa}\).
1.3. Boundary conditions and loads#
With reference to Figure 1-1, the boundary conditions are as follows:
\(\mathit{BAS}\): movements blocked according to \((X)\mathit{et}(Y)\),
\(\mathit{GAUCHE},\mathit{DROITE}\): movements blocked following \((X)\).
The pressure is affected on segment \(\mathit{HAUT}\) via PRES_REP following \((Y)\) and varies as a function of time as follows:
instant \(t\) |
0 |
1 |
\(P(t)\) |
0 |
-0.5x104 |
The pressure is imposed using 5 steps up to 0.2 s and 10 steps up to 10 s.
1.4. Initial conditions#
Zero stresses and deformations.