Closed-form solutions for the contact problem of anisotropic materials indented by two collinear punches

The present paper performs an exact analysis of the contact problem of anisotropic materials indented by two collinear punches. By considering the eigenvalue properties, the real fundamental solutions are given for the roots of the complex conjugate case and the real number case. A singular integral equation reduced from the stated problem is solved exactly for the case of two flat punches and two semi-cylindrical punches. Numerical results are presented to reveal how the interaction of the two punches and the elastic coefficient ratio affect the contact behaviors under the two collinear punches. When two individual rigid punches mingle as one rigid punch, classical results for one rigid punch are obtained, which validates the present derivation.