# Further Development of 3D Crack Growth Simulation Program to Include Contact Loading Situations
## 4 Submodel for Models with Contact Definition between Crack Surfaces
The displacements in the y-direction of the 'driven nodes' that belong to the slave surface should be discarded in order to perform the simulation with contact definitions in the crack surfaces. This procedure can be applied only in cases in which the crack is in any of the principal planes. If the crack is in a slanting position to the principal planes, then the omitting of displacements in one direction cannot be applied. Therefore, to create a more general solution, a new geometry of the submodel is introduced. Adapcrack3D already has the feature of extending element layers in all three directions [7]. By making use of this feature, a new geometry for the submodel is designed and is shown in Figure 10. There are three elements created in all directions from the crack front. The height of the elements close to the crack surfaces are reduced in order to come as close to the crack as possible. This feature is newly implemented in Adapcrack3D, and the user can provide the height of the elements close to the crack surfaces. This can be selected as a percentage of the value, \(l_{\text{s}}\), so that the size of the submodel remains the same as before (Figure 10a). For instance, in the submodel presented in Figure 10, the value of \(l_{\text{s}}\) is 1.0 mm and the height of the smallest element is 0.05 mm (5% of \(l_{\text{s}}\)). As shown in Figure 10b, the nodes on the crack surfaces are not selected as 'driven nodes'. All the nodes that appear on the intersecting surfaces other than the nodes from the crack surfaces are selected as 'driven nodes'. One advantage of this method is that the arranging of 'driven nodes' in different sets is not necessary. Another advantage is the avoidance of 'over constraints' during contact between the crack surfaces. The resulting displacement on the model in the y-direction is displayed in Figure 10c. The results are in good agreement with the reference result in Figure 9c. Figure 9: CT specimen with ‘element sets’ and submodel with different sets of ‘driven nodes’: (a) Global model of CT specimen with ‘element sets’ defined on both sides of the crack; (b) Submodel generated with three different sets of ‘driven nodes’ marked in red, blue, and green; (c) Displacement of the submodel in the y-direction. To validate the results for the newly proposed submodel in Figure 10, the stress intensity factors along the crack front are evaluated. The values calculated with the previous geometry of the submodel, as in Figure 9, are taken as references. The stress intensity factors calculated by Adapcrack3D for both the submodels and the difference between the results are displayed in Figure 11. The simulation is performed for Mode I loading and in Figure 11, the values obtained for the reference model and for the new submodel are displayed in blue and orange, respectively. Because the new submodel has three elements in all directions, Adapcrack3D creates a finer mesh than the reference submodel. As a result, more nodes are present on the crack front for this model and thereby there are more points in orange than in blue. The difference between the results in percentage is shown in Figure 11, being approximately five percent at both ends of the crack front and below two percent in the middle. This shows that, by using the new submodel, the simulation will provide results that are very close to those with the previous submodel. In order to test the new submodel geometry and to define the contact definition between crack surfaces, the model of a CTS specimen is also selected. The model of the CTS specimen and the submodel created are displayed in Figure 5:0 The specimen is modelled with an initial crack, as shown in Figure 12, and the loads applied on it create a Mode  
Figure 5:1 Stress intensity factors calculated by Adapcrack3D for CT specimen and the difference between the results: (**a**). Stress intensity factors along the crack front for Mode I loading of the reference submodel and the new submodel; (**b**) Difference in percentage between the values in Figure 11 along the crack front.