DISSIPATIVE GRAPH SOLUTIONS FOR A 2-DEGREE-OF-FREEDOM QUASI-STATIC FRICTIONAL CONTACT PROBLEM

In this paper we discuss the nature of the quasistatic purely elastic limit to the dynamic viscoelastic solutions to a 2 degree-of-freedom ( d.f.) frictional contact problem. In a significant situation for which a continuous equilibrium path cannot exist in the limit, we show that , when the mass and viscosity coefficients are decreased to zero in an appropriate manner, a connected graph is approached in the 3-dimensio nal space of the displacement components plus the time (load parameter ) variable. This graph solution contains an instantaneous portion, a d isplacement discontinuity with respect to time, along which the total energy dissipated into some external sink is non-negative. These (poss ibly oscillatory and non-equilibrated) instantaneous paths and some of their qualitative features are discussed and compared with those resu lting from quasistatic viscoelastic approximation procedures. For a pa rticular class of graph solutions which may be approached by sequences of either dynamic or quasistatic viscoelastic solutions, we show that a near future evolution of the system does always exist and that the direction of that evolution for the initiation or the continuation of an instantaneous path is uniquely defined.