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The general 3D Hertzian contact problem for anisotropic materials

The general 3D Hertzian contact problem for anisotropic materials
The general 3D Hertzian contact problem for anisotropic materials
This paper presents a general method for solving the 3D frictionless contact problem between generally anisotropic materials with any second order surface geometry. The method uses the Stroh formalism to find the Green's Functions (GF) of the materials with an efficient numerical integration process. The GFs are then expanded in Fourier series in order to solve the Hertzian contact problem between the two bodies as a perturbation to the first order, 2equivante isotropic2, solution to the problem. The latter permits to define an 2equivalent indentation modulus of the contact" which is a single parameter computed from the first terms of the Fourier expansion of the two GFs (ie the average values) and permits to use the standard Hertzian solution: this gives a good approximation to the contact area (at most elliptical in any case) which is approximated as a circle for axi-symmetrical geometry, and for the approach of remote points in the two bodies. The "equivalent indentation modulus", which depends on materials and orientation, is computed for a set of composite materials of practical interest.
anisotropic crystals, composite materials, contact problems
0878498915
221-222
281-292
Trans Tech
Ciavarella, M.
d5aa6350-b3d4-4a78-a670-9d78242f58c5
Demelio, G.
cb38aabe-9837-4ab2-aa87-60028fd7b82c
Schino, M.
4d4604c3-ae65-49a8-bd5d-b600928f558a
Vlassak, J.J.
b937b334-67e7-40c3-8047-d8d5149010d9
Ciavarella, M.
d5aa6350-b3d4-4a78-a670-9d78242f58c5
Demelio, G.
cb38aabe-9837-4ab2-aa87-60028fd7b82c
Schino, M.
4d4604c3-ae65-49a8-bd5d-b600928f558a
Vlassak, J.J.
b937b334-67e7-40c3-8047-d8d5149010d9

Ciavarella, M., Demelio, G., Schino, M. and Vlassak, J.J. (2002) The general 3D Hertzian contact problem for anisotropic materials. In, Experimental Techniques and Design in Composite Materials 5. (Key Engineering Materials (ISSN 1013-9826), 221-222) Switzerland. Trans Tech, pp. 281-292.

Record type: Book Section

Abstract

This paper presents a general method for solving the 3D frictionless contact problem between generally anisotropic materials with any second order surface geometry. The method uses the Stroh formalism to find the Green's Functions (GF) of the materials with an efficient numerical integration process. The GFs are then expanded in Fourier series in order to solve the Hertzian contact problem between the two bodies as a perturbation to the first order, 2equivante isotropic2, solution to the problem. The latter permits to define an 2equivalent indentation modulus of the contact" which is a single parameter computed from the first terms of the Fourier expansion of the two GFs (ie the average values) and permits to use the standard Hertzian solution: this gives a good approximation to the contact area (at most elliptical in any case) which is approximated as a circle for axi-symmetrical geometry, and for the approach of remote points in the two bodies. The "equivalent indentation modulus", which depends on materials and orientation, is computed for a set of composite materials of practical interest.

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More information

Published date: 2002
Keywords: anisotropic crystals, composite materials, contact problems

Identifiers

Local EPrints ID: 22357
URI: http://eprints.soton.ac.uk/id/eprint/22357
ISBN: 0878498915
PURE UUID: 1988d713-53f6-4b27-a09d-1a812bebeaa2

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Date deposited: 24 Mar 2006
Last modified: 16 Dec 2019 19:24

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Contributors

Author: M. Ciavarella
Author: G. Demelio
Author: M. Schino
Author: J.J. Vlassak

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