Impact of cylinder against a rigid wall: impactBar
Prepared by Philip Cardiff and Ivan Batistić
Tutorial Aims
- Demonstrate how to perform a dynamic impact analysis with large deformations and large sliding contact.
Case Overview
In this case, which has been analysed by Cardiff et al. [1], a cylindrical copper bar impacts a rigid wall. The bar has an initial radius of \(r_0 = 3.2\) mm, an initial length of \(l_0 = 32.4\) mm, and an initial velocity of \(v_0 = 227\) m/s. A schematic of the problem geometry is shown in Figure 1. The problem is modelled as axisymmetric.
Figure 1 - Problem geometry [1]
The mechanical properties are given in Table 1. Transient effects are included. A frictionless contact is considered between the rigid ground and the lower boundary of the cylinder. The model is solved in 1000 equally spaced time increments.
Table 1 - Mechanical properties
| Parameter | Symbol | Value |
|---|---|---|
| Young's modulus | \(E\) | \(117\) GPa |
| Poisson's ratio | \(\nu\) | \(0.35\) |
| Initial yield stress | \(\sigma_Y\) | \(400\) MPa |
| Initial density | $\rho$ | $8930$ kg/m$^3$ |
| Hardening modulus | $\kappa$ | $100$ MPa |
Expected Results
The predicted deformed geometry is shown for four separate times in Figure 2. A comparison with the numerical results predicted by Aguirre et al. [2] is available in [1]. Table 2 compares the final end radius of the bar at \(80\) \(\mu\)s, for the finer mesh consisting of 5760 cells, with numerical results from other methodologies [2, 3]. Good agreement is found.
Figure 2 - Predicted deformed geometry [1]
Table 2 - Predicted end radius at \(80\) \(\mu\)s.
| Method | Predicted radius (in mm) |
|---|---|
| [2] FE method - tetrahedra | \(5.55\) |
| [2] FE method - hexahedra | \(6.95\) |
| [2] FE method average nodal pressure | \(6.99\) |
| [1] FV method | \(6.98\) |
| solids4Foam | $7.14$ |
Video 1 - Mesh deformation during impact, coloured by velocity
Running the Case
The tutorial case is located at solids4foam/tutorials/solids/elastoplasticity/impactBar. The case can be run using the included Allrun script, i.e. > ./Allrun.
The Allrun script first creates the blockMeshDict file from system/blockMeshDict.cylinder.m4 using the m4 scripting language. The blockMesh utility is then used to create the mesh. For foam-extend, the axis edges are manually removed using collapseEdges. The setFields utility initialises the old displacement and displacement-increment fields required by the time scheme at the beginning of the simulation. Finally, the case is run using the solids4Foam solver.