Computational Methods for Nonlinear Dynamic Problems in Solid and Structural Mechanics: Progress in the Theory and Modeling of Contact and Friction

摘要

This report summarizes results of research related to the theory and modeling of contact and friction on both rough dry surfaces and on lubricated surfaces. A summary of work on the quality of the numerical analysis of elastohydrodynamic lubrication problems is given. A complete mathematical foundation is established for these problems, new numerical methods are devised, adaptive finite elements schemes are constructed, and a variety of numerical solutions are obtained. A-priori estimates are derived, which are shown to give estimates of rates of convergence in agreement with numerical experiments. A summary of ongoing work and the development of new models of contact and friction on rough surfaces is given. A probabilistic model of rough dry surfaces is described, in which asperity heights are assumed to be randomly distributed over a surface. The effects of inter-molecular adhesion on contact friction are included. This approach allows one to focus on the problem of deformation of a typical asperity. In this work we assume the mechanical response of an asperity to be nonlinear viscoplastic, enabling one to model elastic, viscoelastic, plastic, and viscoplastic response as well as damage of rough surfaces in contact. Preliminary versions of these models are used to study the elasto-dynamic behavior and control of structural components subjected to frictional forces. Numerical results show that the models five excellent agreement with experimental data.