# Further Development of 3D Crack Growth Simulation Program to Include Contact Loading Situations
## 4 Submodel for Models with Contact Definition between Crack Surfaces
In the cross-sectional view in Figure 7c, the red and blue nodes have the same coordinates. As described above, if the nodes that appear in the yellow region are selected as 'driven nodes', then the adjacent red and blue nodes are mapped with the same displacement from the global model and the simulation of the submodel returns incorrect stress distribution. This is evident in Figure 8, which shows the displacements in the model along the principal axes: Figure 8a (displacement along x-axis), Figure 8b (displacement along y-axis), and Figure 8c (displacement along z-axis). Because the crack is loaded in the Mode I direction, the correct result should have been an opened crack. Figure 6: Aspects of a submodel from Adapcrack3D: (**a**) The position of the submodel with respect to the global model; (**b**) The geometry of the submodel with hexahedral mesh with the size of the submodel. In order to avoid this error during simulation, the displacements of the 'driven nodes' in the crack surfaces in the submodel have to be mapped appropriately from the correct side of the crack in the global model. To achieve this, a global model is created with two different 'element sets', each on either side of the crack. The submodel is generated with three different sets of 'driven nodes'. The global model and the submodel are displayed in Figure 9. The sections of the global model to define two 'element sets' on either side of the crack are shown in red and blue in Figure 9a. Figure 9b is the newly generated submodel with three sets of 'driven nodes': (i) nodes marked in red acquire the displacements mapped from the red 'element set' of the global model, (ii) nodes marked in blue acquire the displacement mapped from the blue 'element set' of the global model, and (iii) all other nodes that are on the outer surfaces intersecting the global model are marked in green. All three 'driven nodes' sets are defined in the FE model of the submodel, but in this case the mapping of the 'driven nodes' sets (i) and (ii) from the correct global model 'element set' have to be defined explicitly. Figure 9c is the resulting displacement in the y-direction of the submodel. It is evident in the picture that by applying this method the displacements are correctly mapped, and now the crack is thereby in an opened state. Similarly, the simulations have also delivered correct results for the x- and z-directions. Figure 8: The wrongly mapped displacements on the submodel along the principal axes: (**a**) Along x-axis; (**b**) Along y-axis; (**c**) Along z-axis. Figure 7: Models of CT specimen and the submodel for crack growth simulation: (**a**) Input model of the CT specimen along with the initial crack; (**b**) The submodel generated by Adapcrack3D with the edges of the crack surfaces marked in red and blue; (**c**) The submodel created by Adapcrack3D with the nodes on crack surfaces lying on top of each other. As per the rule, in the FE model of the submodel, the directions (x, y, z) from which the displacements have to be mapped from the global model have to be specified. In the example above, the displacements have been mapped from all three directions. In the case of models with contact definitions between the crack surfaces, the edge nodes on the crack surfaces (marked in red and blue in Figure 9b) are also assigned with contact definitions. The contact definitions in the FE solvers are defined with the master-slave method in which one of the crack surface is the master and the other is selected as the slave. This creates the problem of 'over constraints' in the FE solver, and the simulation will be aborted. For cracks that are created on one of the principal planes (XY, YZ, XZ), this error can be resolved by not mapping the displacements in the direction that is perpendicular to the plane in which the crack lies. For instance, in the above example, the displacements of nodes that are marked as red and blue should be mapped only from the x- and z-directions.