Forces of various nature, e.g. elastic, viscoelastic, plastic forces, are observed during the contact interaction of bodies in the most general case. These forces are reflecting the real structure and the properties of a rough surface. Sliding friction forces and so-called adhesion forces are the main mechanical characteristics to describe contact interaction. They are representing 2D surface constitutive laws in analogy to elasto-plasticity for 3D continua. A key to the generalization of the construction of various interface contact laws (besides e.g. the well known Coulomb friction law) is based on proper combinations of known constitutive relations for elasticity, plasticity, viscosity etc. in completely nonlinear form. These combinations can be obtained with regard to main thermodynamical principles leading to the principle of maximum dissipation expressed in arbitrary surface metrics in covariant form. This leads to a set of a-priori stable numerical algorithms including various combinations of the decoupled interaction in both normal and tangential directions. This part is appearing as the main and novel part of the project because the known numerical algorithms are including mostly modifications of Coulomb friction law and, therefore, only combinations of linear elasticity and linear plasticity for the contact interface. The focus in the project will be on constitutive relations in the tangential direction, where equations for the elastic region - in nonlinear form here representing the tangential adhesion -- reflecting the surface structure -- and plastic laws, also in nonlinear form, represent frictional interaction. An important issue of the project is the verification of these laws based on homogenization and multi-scale techniques. For the micro-level a model with exact asperities possessing a certain global geometrical structure is taken while the derived surface interface model is taken as an average model for the macro-level to achieve a model usable in large scale computations. The keypoint of the verification is that the homogenization procedure in the current project is aiming not only at averaging of in the normal direction leading to the Coulomb friction law, but, as a main focus, at averaging in the tangential direction leading to a new coupled form including tangential adhesion and friction. A set of experiments will be provided to define global macro-characteristics of the developed averaged model such as the structures of the adhesion tensor as well as of the friction tensor.