A Newton-like algorithm to solve contact and wear problems with pressure-dependent friction coefficients

Abstract

This paper extends and improves the Newton algorithm to solve contact and wear problems with pressure-dependent friction coefficients. Especially, the wear problems with pressure-dependent friction coefficients are numerically solved for the first time. The contact forces are calculated by the bipotential method. Combining the calculation steps of contact forces with the local equilibrium equations, the contact and wear problems are described in the local form. The nonlinear equations are solved by a Newton-like algorithm in which the new piecewise continuous contact tangent matrices are explicitly derived. The contact tangent matrices contain the coupled relationship of the friction coefficients and the normal contact pressure. The wear is calculated via the Archard wear law when the global Gauss-Seidel-like iteration is converged. Numerical examples show that different pressure-dependent friction coefficients will affect the pressure distribution, the wear rate and shape of objects, and may result in different wear regimes in some cases.