A Mixed Variational Formulation of a Contact Problem with Wear

Abstract

We consider a mathematical model which describes the sliding frictional contact between a viscoplastic body and an obstacle, the so-called foundation. The process is quasistatic, the material's behavior is described with a viscoplastic constitutive law with internal state variable and the contact is modelled with normal compliance and unilateral constraint. The wear of the contact surfaces is taken into account, and is modelled with a version of Archard's law. We derive a mixed variational formulation of the problem which involve implicit history-dependent operators. Then, we prove the unique weak solvability of the contact model. The proof is based on a fixed point argument proved in Sofonea et al. (Commun.

Study of Carbon Matrix Composite as Wear-Resistant Plate Material on Improving Wear Resistance and Mixing Effect in Mixing Process

“…In the modification process, a large amount of alcohol and water will be produced, which will cause alcohol vapor corrosion on the surface of wear-resistant plate. The addition of silica will increase the viscosity of the rubber, produce adhesion and lagging friction in the mixing process, and also cause wear on the wear-resistant plate [ 15 , 16 , 17 ]. However, the metal powder generated by the surface wear of the wear-resistant plate will enter the rubber mixing process, affecting the quality of silica rubber products.…”