Explicit solution of the frictional contact problem of anisotropic materials indented by a moving stamp with a triangular or parabolic profile

The frictional contact problem of anisotropic materials under a moving rigid stamp is solved exactly. Inside the contact region, the Coulomb friction law is applied. Both Galilean transformation and Fourier transform are employed to get the appropriate fundamental solutions, which can lead to real solutions of physical quantities no matter whether the eigenvalues are real or complex. The complicated mixed boundary value problem is converted to singular integral equations of the second kind, which are solved analytically in terms of elementary functions for either a triangular or a parabolic stamp. Explicit formulae of surface stresses are obtained. Numerical analyses are performed in detail to reveal the surface damage mechanism. It is also found that in the frictionally moving contact problem, the friction coefficient has a more important role than the moving velocity.