An equation of anisotropic friction with sliding path curvature effects

Anisotropy and inhomogeneity of dry friction can induce a dependence of friction force on a sliding path curvature[ The objective of this study is to extend mathematical models of anisotropic friction by including the sliding path curvature e}ects[ Due to this\ a set of independent variables of the friction force constitutive equation is extended\ and a derivative of the sliding velocity unit vector is taken into account[ The friction description is investigated in a general case and in a particular when non!homogeneous friction properties form concentric circles in a contact surface[ It has been found that] the friction constitutive equation and its variables satisfy the axiom of objectivity^ the Second Law of Thermodynamics restricts components of tensors in the constitutive equation^ there are radial and concentric circular privileged sliding directions[ Non!homogeneous friction in the form of concentric circles has the global axial symmetry\ while two tensors in the constitutive equation are de_ned locally and they have orthotropic and anisotropic propertiesrespectively[ The sliding path curvature can induce positive and negative additional friction