Models of kinematics dependent anisotropic and heterogeneous friction

Abstract

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.

On coupled models of anisotropic contact surfaces and their experimental validation

“…Ogden material law for 2D case) can be taken for the adhesion region together with a more complex friction law for the friction region (e.g. see the proposals of He and Curnier [11] and recently Zmitrowicz [31]). The calibration process, in due course, can be provided by experimental investigations as well as by numerical tests involving homogenization processes and multi-scale techniques, for which the methodology for the isotropic case is shown in [1].…”

On the angular velocity slip in nano-flows

“…Let us introduce an auxiliary unit versors: which represent the slip velocity direction and the total angular slip velocity direction, respectively. Assuming a possible form of friction mathematical models and restricting ourselves only to isotropic friction by Zmitrowicz (2006), we postulate, as in the classical Coulomb hypothesis of resistance, that the layer resistance contains three different contributions, i.e. : adherence, laminar and turbulent (skin eddies):…”

Constitutive behaviour of quasi-brittle materials with anisotropic friction

“…Theoretical approaches proposed in recent years involve elegant mathematical formulations Zmitrowicz, 2006), but often need sophisticated laboratory tests to determine material parameters for the identification of the failure domain (Babu et al, 2006).…”

“…A thorough discussion on failure criteria, together with an extended list of references, can be found in the papers by Duveau et al (1998) for geotechnical materials, in the paper by Anthoine (1992) for masonry and in the paper by Zmitrowicz (2006) for a large class of materials (composites, cork, crystals, wood, polymers, ceramics and layer-lattice materials).…”