ON AN EXAMPLE OF NONEXISTENCE OF SOLUTION TO A QUASI-STATIC FRICTIONAL CONTACT PROBLEM

In this paper we consider an example of non-existence of near future q uasistatic evolution for a two degree-of-freedom elastic system in fri ctional contact with a fixed flat obstacle. Precisely for the data con sidered by Klarbring in his earlier presentation of that example, we c onstruct generalized solutions which satisfy all the governing equatio ns and conditions at all times larger than the initial time and that h ave a (possibly non-equilibrated) instantaneous jump at the initial ti me. We establish appropriate forms for the governing force balance equ ations and the frictional contact conditions along that initial jump. For the general case of a two degree-of-freedom elastic system in fric tional contact with a fixed flat obstacle we formulate the problem of finding ''quasistatic'' displacement trajectories which may have disco ntinuities with respect to time and which have a non-negative power di ssipated into some external sink along those jumps. The approximation of the generalized solutions by the solutions to a sequence of quasist atic frictional contact problems with additional viscous damping terms when the damping coefficient decreases to zero is also discussed.