THE BOUNDARY ELEMENT METHOD FOR VISCOELASTIC MATERIAL APPLIED TO THE OBLIQUE IMPACT OF SPHERES

Stephan Kusche

DOI Number
10.22190/FUME1603293K
First page
293
Last page
300

Abstract

The Boundary Element Method (BEM) for elastic materials is extended to deal with viscoelastic media. This is obtained by making use of a similar form of the fundamental solution for both the materials. Some considerations are attributed to the difference of the normal and the tangential contact problem. Both normal and tangential problems are furthermore assumed to be decoupled. Then the oblique impact of hard spheres with an incompressible viscoelastic half-space (linear standard-model) is studied. By assuming stick conditions during impact, one obtains the dependence of the two coefficients of restitution as functions of two input parameters. This result is expressed in an elegant and compact form of the fitting function.

Keywords

Contact Mechanics, Boundary Element Method, Linear Viscoelastic Material, Rebound Test, Oblique Impact, Tangential Problem

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References

Hertz, H., 1882, Über die Berührung fester elastischer Körper, Journal für die reine und angewandte Mathematik, 92, pp. 156-171.

Deresiewicz, H., 1968, A Note on Hertz’s Theory of Impact, Acta Mechanica, 6, pp. 110–112.

Mindlin, R.D., 1949, Compliance of Elastic Bodies in Contact, Journal of Applied Mechanics, 16, pp. 259–268.

Maw, N., Barber, J.R., Fawcett, J.N., 1976, The Oblique Impact of Elastic Spheres, Wear, 38(1), pp. 101–114.

Maw, N., Barber, J.R., Fawcett, J.N., 1977, The Rebound of Elastic Bodies in Oblique Impact, Mechanical Research Communications, 4(1), pp. 17–22.

Maw, N., Barber, J.R., Fawcett, J.N., 1981, The Role of Elastic Tangential Compliance in Oblique Impact, Journal of Lubrication Technology, 103(1), pp. 74–80.

Jäger, J., 1994, Analytical Solutions of Contact Impact Problems, Applied Mechanics Review, 47(2), pp. 35–54.

Lyashenko, I.A., Popov, V.L., 2015, Impact of an elastic sphere with an elastic half space revisited: Numerical analysis based on the method of dimensionality reduction, Sci. Rep., 5, 8479.

Willert, E., Popov, V.L., 2016, Impact of an elastic sphere with an elastic half space with a constant coefficient of friction: Numerical analysis based on the method of dimensionality reduction, Journal of Applied Mathematics and Mechanics (ZAMM), 96(9), pp. 1089-1095.

Hunter, S. C., 1960, The Hertz problem for a rigid spherical indenter and a viscoelastic half-space, Journal of the Mechanics and Physics of Solids, 8(4), pp. 219–234.

Sabin, G. C. W., 1987, The impact of a rigid axisymmetric indenter on a viscoelastic half-space, International Journal of Engineering Science, 25(2), pp. 235–251.

Calvit, H. H., 1967, Numerical solution of the problem of impact of a rigid sphere onto a linear viscoelastic half-space and comparison with experiment, International Journal of Solids and Structures, 3(6), pp. 951–960.

Gasanova, L., Gasanova, P., Talybly, L., 2011, Solution of a viscoelastic boundary-value problem on the action of a concentrated force in an infinite plane, Mechanics of Solids, 46(5), pp. 772–778.

Peng, Y., Zhou, D., 2012, Stress Distributions Due to a Concentrated Force on Viscoelastic Half-Space, Journal of Computation & Modeling, 2(4), pp. 51–74.

Talybly, L., 2010, Boussinesq’s viscoelastic problem on normal concentrated force on a half-space surface, Mechanics of Time-Dependent Materials, 14(3), pp. 253–259.

Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge.

Pohrt, R., Li, Q., 2014, Complete Boundary Element Formulation for Normal and Tangential Contact Problems, Physical Mesomechanics, 17(4), pp. 334-340.

Cho, Y. J., Koo, Y. P., Kim, T. W., 2000, A new FFT technique for the analysis of contact pressure and subsurface stress in a semi-infinite solid, KSME International Journal, 14(3), pp. 331–337.

Liu, S.,Wang, Q., Liu, G., 2000, A versatile method of discrete convolution and FFT DC-FFT for contact analyses, Wear, 243(1-2), pp. 101–111.

Wang, W.Z., Wang, H., Liu, Y.C., Hu, Y.Z., Zhu, D., 2003, A comparative study of the methods for calculation of surface elastic deformation, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 217, 145–154.

Polonsky, I., Keer, L., 1999, A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques, Wear, 231(2), 206–219.

Kusche, S., 2016, Frictional force between a rotationally symmetric indenter and a viscoelastic half-space. ZAMM - Journal of Applied Mathematics and Mechanics, pp. 1-14.

Johnson, K.L., 1955, Surface interaction between elastically loaded bodies under tangential forces, Proc. R. Soc. A., 230, 531-548.

Munisamy, R.L., Hills, D.A., Nowell, D., 1994, Static axisymmetric Hertzian contacts subject to shearing forces, ASME J. Appl. Mech., 61(2), pp. 278–283.




DOI: http://dx.doi.org/10.22190/FUME1603293K

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