## Interaction Set Ups

This article is the first in a short series of contact themed blogs which are aimed at helping you understand the consequences of different interaction set-ups. The blogs cover node to surface and surface to surface contacts. This blog starts with the basics and covers one of the most common pitfalls encountered when creating interactions; incorrect master-slave surface element density for node to surface interactions.

Figure 1 shows the simple 2D model that is used to illustrate the effect of master-slave surface element densities. A 10MPa pressure is applied to the top edge of Part One (Aluminum), the bottom edge of Part Two (Steel) is fixed and a frictionless interaction with “hard contact” is applied between the parts.

Figure 1: example model

### Abaqus

For both the node to surface and surface to surface contacts, the nodes on the slave surface interact with the master surface. Conversely, the master surface nodes do not interact with the slave surface, therefore, master surface nodes are able to pass through the slave surface.

This problem can also be exacerbated if the slave surface is allocated to the larger of the two surfaces, as per Figure 2.

Figure 2: master-slave relationship

#### To avoid this scenario

It is good practice to ensure that the slave surface can conform to the master surface. This can be achieved by following the recommendations in the Abaqus Manual:

1. Ensure that the element density of the slave surface is greater than that of the master surface.
2. Allocate the slave surface to the smaller of the two surfaces.
3. Allocate the master surface to the stiffer body (considering both geometry and material properties).

If it is not possible to achieve all three, precedence should be given to the first two criteria. Figure 3 shows how the contact behaves when the first two criteria are met, but the third is not.

Figure 3: node to surface, slave surface is smaller and has higher element density than master

The image shows that the nodes of Part One do not cross the master surface of Part Two. Part two is conforming to the shape of Part One in a realistic manner.

Figure 4 shows the contact behavior when the master surface element density is greater than the slave surface element density, and the slave surface is larger than the master surface.

Figure 4: node to surface, master surface is smaller and has higher element density than slave

### Multiple Issues

With this type of arrangement it can be seen that there are multiple issues. Firstly, the issue of master nodes passing through the slave surface can be seen at the corners of Part Two.

Secondly, rather than distributing the load across Part Two, the load is concentrated at the five slave nodes that interact with Part Two, causing mathematical singularities that result in exaggerated stresses in these regions.

For illustration purposes, all of the previous examples have used a relatively coarse mesh for one of the parts. In reality, if surface stresses are of interest, the master surface would be refined to a level that is appropriate for the accompanying slave surface.

Figure 5 shows an appropriate node to surface set-up, for a situation where the slave body is stiffer than the master body.

Figure 5: node to surface, slave surface is smaller and has higher element density than master, appropriate master mesh

The advantage of improving the master surface element density is immediately apparent. The edge load in Part One has been moved to the edge of Part Two, and is no longer an artefact of the coarse mesh.

### Previous examples

They have highlighted that the set-up of interactions can have a dramatic effect on the stresses at contacts. In general, when contact stresses are of interest, try to abide by the following basic rules:

• Ideally the slave surface should belong to the smallest surface, with the highest element density and the softest body (considering both structure and material stiffness).
• If not all of the above can be achieved, it is more important to apply the slave to the smallest surface with the higher mesh density.

More contact related blogs will be added to the Technia website soon, and will cover subjects such as surface to surface contacts and the use of quadratic elements at contacts.