On Prandl's lifting equation arising in wear mechanics
Résumé
A sliding wear contact between a rigid punch and an elastic half plane in presence of a thin aggregate film composed of solid debris and a lubricant fluid is studied. The model based on any wear criterion and constitutive law of the film suggested by micromechnanics approximations. The mechanical system is governed by the evolution of the volume fraction of debris, considered as an internal state variable. The key step iterative computations for solving the non linear system of equations is based on the solution of the fundamental integro-differential equation for the compressive normal stress. Uniqueness of the solution of the integrodifferential equation is then proved. It is shown that there is a profound relationship between the latter equation and Prand'l lifting equation in aerodynamics : both equations cn be solved by Chebyshev's series, and experimentally by similar elaectrical setups. Mathematically, it is found that both equations are related to real and imaginary components of some complex potential, respectively, and to weakly adjoint integro-differential oprators.
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