Validation of normal and frictional contact models of spherical bodies by FEM analysis

H Khawaja, K Parvez

Abstract


Contact forces between two spheres are computed, including the contact pressure (normal) and the frictional stress (tangential) using a finite element method (FEM). A CAD model of a part of a sphere was developed. A mesh was created using ANSYS® Solid 186, 20-Noded hexahedral element and analyzed for its sensitivity. ANSYS® Contact 174 and Target 170, 8-Noded surface elements were used. Contact pressure and frictional stress contours were calculated by varying the displacements. Normal and Tangential contact forces were computed by integrating contact pressure and frictional stress over the contact surface. The values obtained for the normal force were compared with the non-linear spring model as given by Hertz [1]. Similarly values of the tangential force were compared with the model of Mindlin and Deresiewicz (MD) [2]. The FEM results were found to be in agreement with the models.

Full Text:

PDF

References


Hertz H., Uber die Beruhrang fester elastischer Korper (On the contact of elastic solids), Journal der rennin und angewandeten Mathematik. 1882, 92, S. 156–171.

Mindlin R. D. & Deresiewicz H., Elastic Spheres in Contact under Varying Oblique Forces, Journal of Applied Mechanics. 1953, 20, 327.

Johnson K. L., Contact Mechanics Second Edition, Cambridge University Press. 1985, New York.

Zhang X. & Vu-Quoc L. An accurate elasto-plastic frictional tangential force-displacement model for granular flow simulations: Displacement-driven formulation, Journal of Computational Physics. 2007, 225, 730-752. CrossRef

Walton O. & Braun R., Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks, Journal of Rheology. 1986, 30 (5), 949-980. CrossRef

Thornton C. & Yin K. K., Impact of elastic spheres with and without adhesion, Journal of Powder Technology. 1991, 65, 153-166.

Multiphysics FEM Package, ANSYS® Inc., Release 11.0

Documentation, Structural Analysis Guide, and Verification Manuals, ANSYS® Inc., Release 11.0

Vu-Quoc L., Zhang X., & Lesburg L., Normal and tangential force-displacement relations for frictional elasto-plastic contact of spheres, International Journal of Solids and Structures. 2001, 38, 6455-6489. CrossRef

Jaeger J., New Solutions in Contact Mechanics, WIT Press Southampton, 2005, Boston.

Anh L. X., Dynamics of mechanical systems with Coulomb friction, Springer-Verlag, 2003, Berlin.




DOI: http://dx.doi.org/10.1260/1750-9548.4.2.175

Copyright (c) 2016 The International Journal of Multiphysics