You may find a recent ASME paper on "Revisiting the Cattaneo–Mindlin Concept of Interfacial Slip in Tangentially Loaded Compliant Bodies" the most relevant to your question.
You cam find this paper here (Transactions of the ASME, 2010, Vol. 132)
In the absence of modern numerical techniques several simplifying assumptions were required by Mindlin. These assumptions include: perfectlyelastic bodies, discontinuous contact condition, which transfersfrom perfect slip during the normal loading into full stick prior toapplying the tangential loading, neglecting the effect of the tan-gential loading on the contact area and contact pressure distribu-tion produced by the normal load, a local Coulomb friction lawthat limits the shear stress at the contact interface, and limitingany slip between the contacting bodies to their contact interfaceonly.
In the ASME paper, some recent theoretical models, which are based on this earlier alternative approach,and in which the simplifying assumptions of the Cattaneo–Mindlin concept were completely relaxed, are described along with their experimental verification. It is shown that the presliding problem between contacting bodies can be accurately solved by these models using realistic physical assumptions and failure criterion.
In addition, you may ask the author, who cited Midline 1949 paper, for the source file you need.
[2] Mindlin, R. D., 1949, “Compliance of Elastic Bodies in Contact,” ASMETrans. J. Appl. Mech.,16, pp. 259–268.
It reviews contact modeling with an emphasis on the forces of contact and their relationship to the geometrical, material and mechanical properties of the contacting bodies, and including reviews on experimental investigations as well as the
dynamics and associated instabilities of sliding contact.
would you mind sending me the paper from Mindlin and Deresiewicz [1953] "Elastic spheres in contact under varying oblique forces" to [email protected]?
I would much appreciate if somebody can send me a copy of "Compliance of elastic bodies in contact", Mindlin (1949) and also the paper mentioned by Anton Manoylov , by Mindlin and Deresiewicz (1953).
I'm currently busy adding the calculations for tangential loads (static and rolling) in my HertzWin software (see online https://www.vinksda.com/toolkit-mechanical-calculations/hertz-contact-stress-calculations/ ). So, I'm looking for this article of Mindlin (1949) too.
Other sources for explicit equations for subsurface stresses are welcome too. Like: Deresiewicz, H. (957), Oblique contact of non-spherical bodies. Trans. ASME, Journal of Applied Mechanics
Jaap Vink , you might refer to the Handbook of Contact Mechanics.
We collected, to the best our knowledge, all explicit analytic solutions given in the literature for general axisymmetric contacts under normal and tangential loading, including subsurface stresses.
The book is published under an Open Access licence in English.
Book Handbook of Contact Mechanics: Exact Solutions of Axisymmetr...