Anisotropic dry friction and unilateral non-holonomic constraints

An extension of the model of Coulomb's friction forces to the case of anisotropic friction, when the friction coefficients depend on the coordinates of the points of the contacting surfaces and their mutual orientation is proposed. The anisotropy can be due both to the properties of one of the contact surfaces (for example, the presence of “furrows” in the contact surface and their orientation), and to the corresponding properties of both contact surfaces and the position of the contact areas on the surfaces of the contacting bodies. When the properties of the surfaces of the interacting bodies are independent of the direction of the relative velocity and the mutual orientation of the bodies, the proposed model is identical with the classical Coulomb dry friction model. One of the models of anisotropic friction, which, in the limiting case when the friction force approaches infinity, reduces to a unilateral ideal unilateral constraint, is discussed.