Asymptotic analysis of a rubber cone dented by a rigid cone

The contact of a rubber cone dented by a rigid cone at the apex is analyzed based on large strain theory. The problem is treated as axially symmetric case, and the contact surface is smooth. The asymptotic equations are derived and solved for shrinking domain and expanding domain, respectively. A special case of this problem is that a rubber half space dented by a rigid cone, for this case the analytical solution is obtained for shrinking domain.