Models of kinematics dependent anisotropic and heterogeneous friction

Anisotropy and heterogeneity of friction and wear can result from anisotropic roughness of engineering surfaces and from anisotropic and heterogeneous microstructures present in many materials (wood, single crystals, ceramics, composites, layer-lattice materials, polymers, biomaterials, monomolecular layers). In sliding surfaces of some materials, kinematics of sliding initiates microstructural and frictional changes. This research deals with advanced constitutive models, which describe evolutions of frictional anisotropy and heterogeneity induced by the sliding kinematics. First-, second- and higher-order constitutive equations of friction are developed with respect to powers of a sliding path curvature. The first-order equation of the friction force has two independent variables: sliding velocity unit vector and its derivative. The second- and higher-order equations are polynomials with respect to odd order tensors composed by the sliding velocity unit vector and the derivative. In the equations, friction tensors of even orders describe anisotropy and inhomogeneity of friction and effects associated with the sliding kinematics. The sliding path curvature generates: (a) an additional resistance to sliding, (b) a constraint force normal to the sliding trajectory. The friction constitutive equations satisfy the axiom of objectivity. A condition of dissipated energy restricts the friction tensors and the radius of curvature. Examples illustrate friction descriptions.