A class of sufficiently small friction coefficients for the uniqueness of the solution of the quasistatic contact problem

The present work is concerned with the quasistatic 2D frictional contact problem between discretized elastic bodies. The problem is formulated as a Linear Complementarity Problem. The basic scope of the paper is to give some simple quantitative criteria which define a range of “sufficiently small” coefficients of friction for which it is assured that the problem has a unique solution. The range of the “sufficiently small” friction coefficients depends on the initial contact state of the nodal pairs. At the beginning of the loading history, a special case may sometimes happen for which these nodal pairs are in geometric contact without reactions. For this case, it is proved that the minimum eigenvalue of a sequence of eigenvalue problems gives the demanded range of “sufficiently small” coefficients. During the loading process, generally, it is possible to reduce the problem to the determination of the minimum eigenvalue of just one eigenvalue problem.