Contact Friction Models and Stability Problems
The present lecture notes are devoted to two important aspects of contact interaction, namely the constitutive modelling of slip and friction rules and stability conditions. In considering normal and tangential contact tractions and the conjugate elastic and slip displacements, only elastic-frictional response is considered, thus neglecting plastic asperity interaction and the related phenomena of asperity flattening or crushing. However, the anisotropy of contact asperities was accounted for and the respective frictional slip and wear rules are considered. Next, for a nonuniform contact interaction, the evolution of slip zones is discussed for two simple cases of an elastic strip interacting with the frictional foundation and two interacting spheres under normal and tangential loading. The slip and memory rules require introduction of consecutive active loading and memory surfaces in order to describe properly the friction hysteresis phenomena. The description is very similar to that used in the plasticity theory for modelling elasto-plastic cyclic response of materials.
KeywordsTangential Force Frictional Contact Dissipation Function Slip Zone Incremental Relation
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- Hoff, N.J. (1949). Dynamic criteria of buckling. In Engineering Structures, pp. 121–139. Academic Press, New York.Google Scholar
- Jarzebowski, A.: On the modelling of fibre pull-out forces in composites. In: Brittle matrix composites,vol. 1 (Brandt, A. M., Marshall, I. H., eds.), pp. 371–381. Amsterdam: Elsevier 1986.Google Scholar
- Jarzebowski, A., Mroz, Z.: A constitutive model for sands and its application to monotonic and cyclic loadings. In: Proc. Int. Workshop Constitutive equations for granular non-cohesive soils, Cleveland 1987, pp. 307–323. Rotterdam: Balkema 1989.Google Scholar
- Kerr, A.D. (1973). A model study for vertical track buckling. High Speed Ground Transp. Jl 7, 351–368.Google Scholar
- Mroz, Z., Norris, V. A.: Elastoplastic and viscoplastic constitutive models for soils with application to cyclic loadings. In: Soils under cyclic and transient loads, pp. 173–217. Chichester: Wiley 1982.Google Scholar
- Nguyen, Q.S. (1992). Bifurcation and stability in dissipative media (plasticity, friction, fracture), ASME Appl. Mech. Revs., 47, 1241–1253.Google Scholar
- Piekarski, J., Mroz, Z., 2001. Critical and Postcritical States of Elastic Systems with Unilateral Frictional Contact. Submitted for Eur. J. Mechanics A/Solids.Google Scholar
- Zmitrowicz, A. (1987). A thermodynamical model of contact, friction and wear: I governing equations, II constitutive equations for materials and linearized theories, III constitutive equations for friction, wear and frictional heat. Wear 114, 135–168, 169–197, 199–221.Google Scholar