7. Conclusions and final remarks

The main contributions in the field of contact mechanics were demonstrated along this chapter applied for an important specific system, sphere-plane contact, in which several hardness tests are performed.

Clearly, there is a lack in the experimental demonstration of theories presented. This is an interesting challenge, as the numerical simulation increases at much higher speed than the experimental results.

An updated value obtained through numerical simulation for the differential hardness is 1.7, different from that predicted by Tabor (2.5). Certainly, an experimental demonstration could be elucidating this difference.

In addition, the hardening and friction effects on the sphere-plane system can be more explored through both numerical simulations and experimental arrangements.
