Asymptotic solution of the contact problem for a thin elastic layer

Tribological Modeling

“…In the past, both, solution to the contact problem and stress distribution in the coating as a function of the prescribed boundary loading have been attempted. The solution to the contact pressure profile in the case of cylindrical contact between coated elastic solids has been obtained to varying degrees of sophistication by a number of investigators [1][2][3][4][5][6]. Most of the early work [1][2][3][4][5] considered an asymptotic problem of a very thin or thick coating.…”

“…The solution to the contact pressure profile in the case of cylindrical contact between coated elastic solids has been obtained to varying degrees of sophistication by a number of investigators [1][2][3][4][5][6]. Most of the early work [1][2][3][4][5] considered an asymptotic problem of a very thin or thick coating. Meijers [3], while considering an elastic layer over a rigid substrate demonstrated that the solutions for a thin and thick layer overlap so well that these solutions may apply to arbitrary layer thicknesses with excellent approximation.…”

Numerical Methods of Solution of Contact Problems in Layered Media

“…The case of a spherical punch is somewhat more complicated [2]. He approximated the integrand of the kernel of the integral equation (15) as (in our notation) where B and C are new elastic constants to be determined from the conditions…”

“…where E (1) , v (1) and E (2) , v (2) are the modulus of elasticity and Poisson coefficient of the layer and the foundation, respectively.…”

“…where H (1) and H (2) are the H parameters (see [3]) for the layer and the foundation, respectively. In the case of rigid foundation H (2) = 0 and formula (10) transforms into (4).…”