4.3. Performance of the approach when adaptive mesh refinement is performed both inside and outside the true contact area

In this section, the performance of the proposed approach when adaptive refinement is also performed inside the true contact area is illustrated. To do so, the contact problems defined by cases of study I and II are solved under several configurations of the approach, in which wmax has been varied, keeping Luni < Lmax (setting 3 in Section 3.1). Figures 10e, f and 12b show examples of the resulting contact area and pressure element mesh that have been obtained for cases of study I and II under this setting of the approach.

The contact pressure distributions along the principal axes of the contact area of the solutions shown in Figure 10d-f are shown in Figure 11b. The contact pressure distributions along the principal axes of the contact area of the solutions shown in Figure 12a, b are shown in Figure 13. It both cases, it can be observed that increasing the value selected for wmax implies that a coarser mesh is used in those regions of the true contact area where the contact pressure

Figure 12. Axisymmetric representation of the resulting contact area and pressure element mesh obtained for CoSII under two different configurations of the approach.

Figure 13. Contact pressure distribution for CoSII under several configurations of the approach.

gradient is small, without a significant loss of accuracy when describing the contact pressure distribution.

The obtained results show that the accuracy of the approach to predict the size of the true contact area does not depend on the value selected for wmax, since the same values are obtained regardless of the value selected for this parameter. This is because when wmax < 1, the accuracy in which the border of the contact area is computed depends only on the value selected for Lmax, as stated in Section 3.2.

Finally, comparing the computational cost of the solutions shown in Figure 10d and e (and Figure 12a and b), it can be observed that a further reduction of the computational cost can be achieved by specifying values of wmax > 0. Although this reduction is not as important as the one achieved by maximizing Lmax � Luni (discussed in Section 4.2), it still can help to reduce the computational cost of the approach.
