Bounding Box Approach

The bounding box insertion method selects proposed cohesive edges by first categorizing the system by three main regions (Figure 2.22): a non-cohesive region where no cohesive element is present, a passive cohesive region where cohesive elements are present but have not undergone any failure, and an active cohesive region where cohesive elements are failing. Failing cohesive element are defined by the value of the strength parameter, $S$, introduced in Equation2.1, which decreases as the element fails until complete failure for $S = 0$.

Figure 2.22: Bounding box method.

The bounding box approach first determines the extent of the active cohesive region. This box is then enlarged by a prescribed amount and new cohesive elements are inserted within this new box. The region between the original and new bounding boxes is the passive cohesive region where failure is expected to occur in the near future. The bounding box will continue to grow and move as long as cohesive elements are failing within the system. The bounding box method is quite capable of determining the appropriate cohesive regions although this method is not self-starting. Instead, at least one cohesive element must be present in the critical region, since the bounding boxes are only defined based on existing cohesive elements. As a result, we are again limited to known problems where critical regions are predictable, such as fracture problems involving a pre-existing notch.

The second drawback of the bounding box approach is that the bounding box may become very large while the actual active cohesive region may be quite small. This situation can occur for problems that have multiple critical regions which are spaced far apart, as in a double notched specimen shown in Figure 2.23. When a single bounding box approach is used, the extent of the failing elements define a box which can cross non-cohesive regions. The resulting enlarged box requires that the non-cohesive region be made cohesive even though failure is not expected there until much later in the simulation, if at all. This may cause insertion to grow uncontrollably, filling the entire domain within a short time.

Figure 2.23: Multiple active cohesive regions.