A numerical solution to the cattaneo-mindlin problem for viscoelastic materials

Abstract

The problem of the frictional mechanical contact with slip and stick, also referred to as the Cattaneo-Mindlin problem, is an important topic in engineering, with applications in the modeling of particle-flow simulations or in the study of contact between rough surfaces. In the frame of Linear Theory of Elasticity, accurate description of the slip-stick contact can only be achieved numerically, due to mutual interaction between normal and shear contact tractions. Additional difficulties arise when considering a viscoelastic constitutive law, as the mechanical response of the contacting materials depends explicitly on time. To overcome this obstacle, an existing algorithm for the purely elastic slip-stick contact is coupled with a semi-analytical method for viscoelastic displacement computation. The main advantage of this approach is that the contact model can be divided in subunits having the same structure as that of the purely elastic frictionless contact model, for which a well-established solution is readily available. In each time step, the contact solver assesses the contact area, the pressure distribution, the stick area and the shear tractions that satisfy the contact compatibility conditions and the static force equilibrium in both normal and tangential directions. A temporal discretization of the simulation windows assures that the memory effect, specific to both viscoelasticity and friction as a path-dependent processes, is properly replicated.