Static frictional indentation of an elastic half-plane by a rigid unsymmetrical punch (Q1332258)

A rigid two-dimensional punch of curved profile with no concave regions and no end-point corners is pressed into an half-plane. The Coulomb- frictional contact shear stress changes its sign along the contact length. The authors prove that this sign change creates a singularity of power type at the reversal point. The contact stress is determined by solution of a Riemann-Hilbert problem, while the unspecified lengths of the shear stress with different directions of acting are determined numerically by solving a system of nonlinear equations containing integrals. The cases of a wedge and of a parabolic punch are numerically analyzed.