THE RIGID PUNCH PROBLEM WITH FRICTION USING VARIATIONAL-INEQUALITIES AND LINEAR COMPLEMENTARITY

The problem of indentation, with friction, of a rigid punch into an elastic half-plane is solved using Green's functions. The problem is stated in terms of variational inequalities and discretized in both time and space. The discrete variational inequalities are then shown to be equivalent to an incremental problem, which after some additional reformulation can be solved as a linear complementarity problem. As is expected, friction effects make the problem load-path dependent, as shown by several numerical examples. The tangential stresses, in particular, show considerable load-path dependence.