We solve a two-dimensional contact problem of wear of an elastic half space by a rigid punch. The punch moves with constant velocity, crushes inhomogeneities of the surfaces, and rubs out the half space. Outside the punch the surface of the half space is unloaded. The solution of the problem of the theory of elasticity is constructed by using Fourier integral transformations. Contact stresses are sought in the form of a Fourier series whose coefficients satisfy dual integral equations which can be reduced to a system of nonlinear algebraic equations for unknown coefficients. We also analyze the dependences of contact stresses, wear, and abrasion on time.
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Levyts'kyi, V.P., Onyshkevych, V.M. & Yas'kevych, I.T. Plane contact problem of wear. Mater Sci 31, 461–466 (1996). https://doi.org/10.1007/BF00559140
- Integral Equation
- Fourier Series
- Algebraic Equation
- Constant Velocity