The vast majority of our analysis work, both support and consultancy, involves the use of contacts in the form of interactions. Their setup and consequent behavior can have a significant effect on the results of an analysis, and therefore it is important that their various incarnations are fully understood. It may seem like a simple subject, but there are some common contact-related pitfalls to avoid during both preprocessing and post-processing.
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 a simple 2D model that is used to illustrate the effect of master-slave surface element densities. A 10 MPa 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
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:
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 the 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 the slave.
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 artifact of the coarse mesh.
They have highlighted that the setup 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.