Viscoelastic contact/impact rheological models

Abstract

The first part of this chapter is dedicated to the analysis of viscoelastic and viscoelasto-plastic rheological contact models (linear and nonlinear parallel spring-dashpot assemblies). The linear spring-dashpot model is studied, and a detailed survey of nonlinear models (like Simon-Hunt-Crossley model and its many variations) as well as other types of assemblies with dry friction elements is made. Emphasis is put on the model’s well-posedness, where complementarity systems may be used as a nice mathematical framework. The second part presents some well-posedness results (existence and uniqueness of solutions) of Lagrange dynamics with unilateral constraints and impacts, considering them as the limit of compliant systems when contact stiffness grows unbounded.