Mathematical modeling of wear-resistance processes of bodies with coatings

We study a mathematical formulation of problems of contact interaction of coated bodies when the material is worn. We state the physical relations that connect the intensity of wear with the characteristic physical quantities. For the case of a half-plane with a thin elastic coating the problem is reduced to singular integro-differential equations whose solution is obtained in the class of orthogonal polynomials. We give estimates of the influence of the characteristics of the coating and the base on the wear process. One figure, two tables.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 51–55.