Sub-discretized surface model with application to contact mechanics in multi-body simulation

The mechanics of contact between rough and imperfectly spherical adhesive powder grains are often complicated by a variety of factors, including several which vary over sub-grain length scales. These include several traction factors that vary spatially over the surface of the individual grains, including high energy electron and acceptor sites (electrostatic), hydrophobic and hydrophilic sites (electrostatic and capillary), surface energy (general adhesion), geometry (van der Waals and mechanical), and elasto-plastic deformation (mechanical). For mechanical deformation and reaction, coupled motions, such as twisting with bending and sliding, as well as surface roughness add an asymmetry to the contact force which invalidates assumptions for popular models of contact, such as the Hertzian and its derivatives [H. Hertz, Über die Berührung fester elastische körper. Journal für die reine und angewandte Mathematik 1882; 92: 156-171; R.D. Mindlin, Compliance of elastic bodies in contact. Journal of Applied Mechanics 1949; 71: 259-268; R.D. Mindlin, H. Deresiewicz, Elastic spheres in contact under varying oblique forces. Journal of Applied Mechanics 1953; 20: 269-286], for the non-adhesive case, and the JKR [K.L. Johnson, K. Kendall, A.D. Roberts, Surface energy and the contact of elastic solids. Proceedings of the Royal Society of London 1971; 324: 301-313] and DMT [B.V. Derjaguin, V.M. Muller, Y.P. Toporov, Effect of contact deformations on the adhesion of particles. Journal of Colloid and Interface Science 1975; 53: 314-326] models for adhesive contacts. Though several contact laws have been offered to ameliorate these drawbacks, they are often constrained to particular loading paths (most often normal loading) and are relatively complicated for computational implementation. This paper offers a simple and general computational method for augmenting contact law predictions in multi-body simulations through characterization of the contact surfaces using a hierarchically-defined surface sub-discretization. For the case of adhesive contact between powder grains in low-stress regimes, this technique can allow a variety of existing contact laws to be resolved across scales, allowing for moments and torques about the contact area as well as normal and tangential tractions to be resolved. This is especially useful for multi-body simulation applications where the modeler desires statistical distributions and calibration for parameters in contact laws commonly used for resolving near-surface contact mechanics. The approach is verified against analytical results for the case of rough, elastic spheres.

The mechanics of contact between rough and imperfectly spherical adhesive powder grains are often complicated by a variety of factors. This paper offers a simple and general method for augmenting contact law predictions in multi-body simulations using a hierarchically-defined surface description for an arbitrary number of properties. This is applied to surface asperities and compared with Archard’s model.Figure optionsDownload as PowerPoint slide