Non-unique slipping in the coulomb friction model in two-dimensional linear elasticity

This work is concerned with the Coulomb friction model in continuum linear elastostatics. We consider the two-dimensional problem and we recall that an infinity of solutions corresponding to slip may exist when the friction coefficient (or its opposite value) is an eigenvalue of a specific problem. We show that such coefficients exist and we determine them explicitly for a simple class of problems. Finally, we exhibit cases in which the static friction problem admits an infinity of solutions slipping in the same direction.