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The paper deals with analysis of selected soft-contact problems in discrete mechanical systems. Elastic-dissipative rheological schemes representing dampers as well as the notion of unilateral constraints were used in order to model interaction between colliding bodies. The mathematical descriptions of soft-contact problems involving variational inequalities are presented. The main finding of the paper is a method of description of soft-contact phenomenon between rigid object and deformable rheological structure by the system of explicit nonlinear differential-algebraic equations easy for numerical implementation. The results of simulations, that is, time histories of displacements and contact forces as well as hysteretic loops, are presented.

Mathematical Formulation of Soft-Contact Problems for Various Rheological Models of Damper