For general contact ABAQUS/Explicit enforces contact constraints using a penalty contact method, which searches for node-into-face and edge-into-edge penetrations in the current configuration. The penalty stiffness that relates the contact force to the penetration distance is chosen automatically by ABAQUS/Explicit so that the effect on the time increment is minimal yet the penetration is not significant.

For surface-to-surface contact ABAQUS/Explicit uses a kinematic contact formulation by default that achieves precise compliance with the contact conditions using a predictor/corrector method. The increment at first proceeds under the assumption that contact does not occur. If at the end of the increment there is an overclosure, the acceleration is modified to obtain a corrected configuration in which the contact constraints are enforced. The predictor/corrector method used for kinematic contact is discussed in more detail in “Contact formulation for ABAQUS/Explicit contact pairs,” Section 29.4.4 of the ABAQUS Analysis User's Manual; some limitations of this method are discussed in “Common difficulties associated with contact modeling using the contact pair algorithm in ABAQUS/Explicit,” Section 29.4.6 of the ABAQUS Analysis User's Manual.

The normal contact constraint for contact pairs can optionally be enforced with the penalty contact method, which can model some types of contact that the kinematic method cannot. For example, the penalty method allows modeling of contact between two rigid surfaces (except when both surfaces are analytical rigid surfaces). When the penalty contact formulation is used, equal and opposite contact forces with magnitudes equal to the penalty stiffness times the penetration distance are applied to the master and slave nodes at the penetration points. The penalty stiffness is chosen automatically by ABAQUS/Explicit and is similar to that used by the general contact algorithm. The penalty stiffness can be overridden for surface-to-surface contact interactions by specifying a penalty scale factor or a “softened” contact relationship.

In the pure master-slave approach one of the surfaces is the master surface and the other is the slave surface. As the two bodies come into contact, the penetrations are detected and the contact constraints are applied according to the constraint enforcement method (kinematic or penalty). Pure master-slave weighting (regardless of the constraint enforcement method) will resist only penetrations of slave nodes into master facets. Penetrations of master nodes into the slave surface can go undetected, as shown in Figure 12–32, unless the mesh on the slave surface is adequately refined.

Balanced master-slave contact simply applies the pure master-slave approach twice, reversing the surfaces on the second pass. One set of contact constraints is obtained with surface 1 as the slave, and another set of constraints is obtained with surface 2 as the slave. The acceleration corrections or forces are obtained by taking a weighted average of the two calculations. For kinematic balanced master-slave contact a second correction is made to resolve any remaining penetrations, as described in “Contact formulation for ABAQUS/Explicit contact pairs,” Section 29.4.4 of the ABAQUS Analysis User's Manual. The balanced master-slave contact constraint when kinematic compliance is used is illustrated in Figure 12–33.

The general contact algorithm uses balanced master-slave weighting whenever possible; pure master-slave weighting is used for general contact interactions involving node-based surfaces, which can act only as pure slave surfaces. For the contact pair algorithm ABAQUS/Explicit will decide which type of weighting to use for a given contact pair based on the nature of the two surfaces involved and the constraint enforcement method used.

Because it is possible for a node on one contact surface to contact any of the facets on the opposite contact surface, ABAQUS/Explicit uses sophisticated search algorithms for tracking the motions of the contact surfaces. While the contact search algorithm is transparent to the user and is rarely a concern, some situations require special consideration and an understanding of the methods. The discussion that follows applies to contact pair interactions. The general contact algorithm uses a somewhat more sophisticated global/local tracking approach that does not require user control.

At the beginning of each step an exhaustive, global search is conducted to determine the closest master surface facet for each slave node of each contact pair. This search is aided by a “bucket sort,” but the cost of a global search is relatively high. A global search is performed only every 100 increments by default. Figure 12–34 shows the global search to determine which of all of the facets on the master surface is the closest facet to slave node 50. The search determines that the closest master facet is the face of element 10. Node 100 is determined to be the node on that master facet that is closest to slave node 50; therefore, it is designated as the tracked master surface node. The goal of the global search is to determine the closest master facet and a tracked master surface node for each slave node.

Since the cost of each global search is relatively high, a less expensive local search is performed in most increments. In a local search a given slave node searches only the facets that are attached to the previous tracked master surface node to determine the closest facet. In Figure 12–35 the slave surface of the model shown in Figure 12–34 has moved since the previous increment. (The relative incremental motion shown is much greater than typically occurs in an explicit dynamic analysis because of the small time increments used.) Since the previous tracked master surface node was 100, the nearest master surface facet of those attached to node 100 (facets 9 and 10) is determined.

Since the time increments are very short, for most situations the contacting bodies move a very small amount from one increment to the next, and the local contact search is adequate to track the motion of the contact surfaces. However, there are certain situations that may cause the local contact search to fail. One such situation, illustrated in Figure 12–36, is a master surface containing a hole.

Another option is to allow a single surface to contact itself. For example, the inside of a tube could be defined as a single surface, which contacts itself as the tube is crushed. Due to the generality and complexity of single-surface contact with the contact pair algorithm, a global contact search is performed every few increments, making single-surface contact significantly more expensive than two-surface contact.

When you define a surface-to-surface contact interaction, you must decide whether the magnitude of the relative sliding will be small or finite. The default (and only option for general contact interactions) is the more general finite-sliding formulation. The small-sliding formulation is appropriate if the relative motion of the two surfaces is less than a small proportion of the characteristic length of an element face. Using the small-sliding formulation when applicable results in a more efficient analysis.