Yes. The manner of which two surfaces in contact interact is highly investigated by the Tribology community.In particular, the field exploring the mechanics of the interaction is called contact mechanics.
Tackling problems of contact mechanics analytically/numerically is often done by solving the elasticity equations. By predicting quantitatively the forces and deformation of the bodies in contact, the coefficient of friction can be calculated. Many analytical\Numerical work have been done up to now, starting from Hertz's groundbreaking solution to more advanced solutions