Contact
Contact Search
| Parameter | Unit | Description |
|---|---|---|
| Contact Radius | $[m]$ | Radius to get a list of potential contact pairs. |
| Master | $[-]$ | Block ID of the master nodes. |
| Slave | $[-]$ | Block ID of the slave nodes. |
Initialization
- Step 1 -
Identification of all surface nodes of contact blocks.
- Step 2 -
All surface nodes are stored in a list. This list exists at all cores with the current position of the surface nodes.
- Step 3 -
Connect each surface node to a geometrical surface.
The standard way for points in the parallelization is given here.
\[\begin{bmatrix}1 \\ 2 \\ 3 \\ 4 \\ 5 \\ 6 \\ 7 \end{bmatrix}_{all}\rightarrow\begin{matrix} \begin{bmatrix} 4 \\ 6 \end{bmatrix}_{C1-global}\\ \begin{bmatrix}1 \\ 2 \\ 7 \end{bmatrix}_{C2-global}\\ \begin{bmatrix}3\\5\end{bmatrix}_{C3-global}\end{matrix}\leftarrow \rightarrow\begin{matrix} \begin{bmatrix} 1 \\ 2 \end{bmatrix}_{C1-local}\\ \begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix}_{C2-local}\\ \begin{bmatrix}1\\2\end{bmatrix}_{C3-local}\end{matrix}\]
A new mapping is needed to the contact surface exchange list. The local numbering (right above) has to be mapped to the sublist and vice, versa.
\[\begin{bmatrix}1 \\ 2 \\ 6 \\ 7 \end{bmatrix}_{surface}\leftarrow\rightarrow \begin{bmatrix}1 \\ 2 \\ 3 \\ 4 \end{bmatrix}_{surface}\rightarrow \begin{matrix} \begin{bmatrix} 6 \end{bmatrix}_{C1}\\ \begin{bmatrix}1 \\ 2 \\ 7 \end{bmatrix}_{C2}\\ \begin{bmatrix}\,\,\,\,\end{bmatrix}_{C3}\end{matrix}\leftarrow \rightarrow\begin{matrix} \begin{bmatrix} 2 \end{bmatrix}_{C1-local}\\ \begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix}_{C2-local}\\ \begin{bmatrix}\,\,\,\,\end{bmatrix}_{C3-local}\end{matrix}\]
List mapping To fill the postion vector with the needed values mappings are needed.
local point ids -> global point id -> reduced contact block point id The mapping has to be done in both directions, because the contact forces have to be applied to the local core point id.
Computation
- Step 1-
Perform a nearest neighbor search with a user defined Contact Radius. The result is a list of potential contact pairs.
- Step 2 -
The surfaces and the polyeder is updated, due to deformation and the surface normals can be computed.
- Step 3 -
Check if the master point lies inside the polyeder. If so connect this point with the surface normal and its nearest neighbor.
Synchronization All cores (except core 1) send it's displacement values to core 1. Core 1 sends them back.
Smaller contact areas are more efficient in numerical analysis, because less synchronisation have to occur.
Contact Models
| Contact Model | Penalty Contact |
|---|---|
| Contact Stiffness | ✔️ |
Penalty Contact
A bond-based contact formulation is computed. The contact stiffness $ c_{contact}$ is defined in YAML input file. Based on that utilzing the horizon $\delta$ the penalty stiffness shown in the table is computed. These parameter are comparable to the bond-based formulation.
| Dimension | Penalty Stiffness |
|---|---|
| plane strain: | $c_{Penalty} = \frac{48 c_{contact}}{\pi 5 \delta_{slave}^3}$ |
| plane stress: | $c_{Penalty} = \frac{9 c_{contact}}{\pi \delta_{slave}^3}$ |
| 3D: | $c_{Penalty} = \frac{12 c_{contact}}{\pi \delta_{slave}^4}$ |
The distance is currently computed as
\[d = |\underline{\mathbf{Y}}_{master}-\underline{\mathbf{Y}}_{slave}|\]
The normal is
\[\mathbf{n} = \frac{\underline{\mathbf{Y}}_{master}-\underline{\mathbf{Y}}_{slave}}{d}\]
Both can be adopted if needed. Utilizing the contact radius $r_{contact}$ the contact force densities are
\[\mathbf{f}_{master} = c_{Penalty}\frac{(r_{contact}-d)}{\delta_{slave}}\mathbf{n}V_{slave}\]
\[\mathbf{f}_{slave} = -c_{Penalty}\frac{(r_{contact}-d)}{\delta_{slave}}\mathbf{n}V_{master}\]
Within PeriLab the functions computemasterforcedensity and computeslaveforcedensity are used to apply the force to the correct postions. This is needed, becaus if a parallel process is run, master and slave nodes not necessarily are on the same core.