Pressing a Long Cylinder: cylinderCrush
Prepared by Philip Cardiff and Ivan Batistić
Tutorial Aims
- Demonstrate a large-strain elastoplastic analysis with frictionless solid contact.
A hyperelastic version of this tutorial is also available in solids4foam attutorials/solids/hyperelasticity/cylinderCrush.
Case Overview
This case considers a long solid cylinder crushed between two rigid plates, as shown in Figure 1. The cylinder diameter is \(0.4\) m, and the cylinder is compressed by half of its diameter. Because the problem is symmetric, only one quarter of the cylinder is modelled. The rigid plate in the computational domain is displaced by \(0.1\) m over 30 equal loading increments.
The plate-cylinder contact is modelled using the solidContact boundary condition with a frictionless contact law. Gravity and transient effects are neglected, so the case is solved as a quasi-static 2-D plane-strain problem. The updated Lagrangian solid model is selected in constant/solidProperties using nonLinearGeometryUpdatedLagrangian.
Figure 1 - Solid cylinder compressed between two rigid plates
The cylinder is modelled using the neoHookeanElasticMisesPlastic mechanical law. The mechanical properties are given in Table 1, and the tabulated hardening curve is given in Table 2. The hardening data is the same as in the elastoplasticity/pipeCrush tutorial and was taken from Cardiff et al. [1].
Table 1 - Mechanical properties
| Parameter | Symbol | Value |
|---|---|---|
| Young's modulus | \(E\) | \(186\) GPa |
| Poisson's ratio | \(\nu\) | \(0.3\) |
| Initial yield stress | \(\sigma_Y\) | \(241.32\) MPa |
| Initial density | \(\rho\) | \(7800\) kg/m\(^3\) |
Table 2 - Hardening behaviour
| Plastic strain | Yield stress (in MPa) |
|---|---|
| \(0.000\) | \(241.32\) |
| \(0.0035\) | \(275.79\) |
| \(0.0083\) | \(301.65\) |
| \(0.0133\) | \(318.88\) |
| \(0.0182\) | \(344.74\) |
| \(0.0281\) | \(361.98\) |
| \(0.0380\) | \(379.21\) |
| \(1.000\) | \(1482.37\) |
Expected Results
Figure 2 shows the initial mesh and the deformed mesh coloured by the von Mises stress field at an intermediate loading step and at the final loading step.
Figure 2 - Initial and deformed meshes coloured by von Mises stress
The solidForces and solidPointDisplacement function objects are added in system/controlDict. They record the contact force on the cylinderContact patch and the displacement of the point at (0 0.2 0), respectively. These outputs can be used to plot the contact force as a function of the plate displacement. Reference force-displacement data is not available in the literature for direct comparison.
Running the Case
The tutorial case is located at solids4foam/tutorials/solids/elastoplasticity/cylinderCrush. The case can be run using the included Allrun script, i.e. > ./Allrun.
The Allrun script creates the mesh using blockMesh and then runs the solids4Foam solver.