1. Reference problem#
1.1. Geometry#
It is a cylinder section in the case of axially symmetric models or a quarter of a cylinder (symmetries) in the case of 3D models. The height of the cylinder is \(H=15\text{mm}\), the inner radius is \({R}_{i}=50\text{mm}\) and the outer radius is \({R}_{e}=100\text{mm}\).
1.2. Material properties#
The material obeys the law of elastoplastic behavior with isotropic work hardening VMIS_ISOT_NLavec as characteristics:
\(E=195000\text{MPa}\) |
Young’s module |
\(\mathrm{\nu }=0.3\) |
Poisson’s ratio |
\({R}_{0}=490\text{MPa}\) |
Work hardening (constant term) |
\({R}_{H}=3000\text{MPa}\) |
Work hardening (linear term) |
\({R}_{1}=60\text{MPa}\) |
Work hardening (exponential term 1) |
\({\mathrm{\gamma }}_{1}=8500\) |
Work hardening (exponential term 1) |
\({R}_{2}=250\text{MPa}\) |
Work hardening (exponential term 2) |
\({\gamma }_{2}=10\) |
Work hardening (exponential term 2) |
\({R}_{K}=50\text{MPa}\) |
Work hardening (power term) |
\({p}_{0}={10}^{-3}\) |
Work hardening (power term) |
\({\gamma }_{m}=0.15\) |
Work hardening (power term) |
1.3. Boundary conditions and loads#
It is a load of imposed forces. They are exerted at the edges and in the volume according to the formulas of the analytical solution. This loading is completed by a minimum boundary condition to block the movement of vertical rigid bodies (a point on the circumference is blocked vertically at the intersection of the lower face and the inner wall), as well as the symmetry conditions in 3D models.
1.4. Initial conditions#
Natural initial conditions (zero internal variables, zero deformations).