Contact Problem for a Rectangular Punch on the Porous Elastic Half-Space
Source abstract
Abstract
The paper is concerned with a contact problem about rigid rectangular punch forced into a half-space made of a linear elastic isotropic material with voids. We use a Cowin–Nunziato model for the half-space, and reduce the problem to a double Fredholm integral equation of the first kind. Then we apply two different approaches, to solve this equation. The first one is based on a direct collocation numerical technique. The second method is asymptotic, and we use a small parameter that is the relative width of the punch. Finally, compliance of the punch is determined, and results of the two different methods are compared with each other, as well as with a Sivashinsky–Panek–Kalker solution.
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Research context
OpenAlex topics: Elasticity and Wave Propagation · Contact Mechanics and Variational Inequalities · Geotechnical and Geomechanical Engineering
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References (13)
Show source-provided references
1. I.N. Sneddon, Mixed Boundary Value Problems in Potential Theory. North-Holland, Amsterdam; Wiley, New York (1966).
2. N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen (1953).
3. S.C. Cowin and J.W. Nunziato, Linear elastic materials with voids. J. Elasticity 13 (1983) 125?147.10.1007/BF00041230 ↗
4. A. Scalia and M.A. Sumbatyan, Contact problem for porous elastic half-plane. J. Elasticity 60 (2000) 91?102.10.1023/A:1010880823544 ↗
5. A. Scalia, Contact problem for porous elastic strip. Internat. J. Engrg. Sci. 40 (2002) 401?410.10.1016/S0020-7225(01)00070-2 ↗
6. G.I. Sivashinsky, The problem of a slender die. J. Elasticity 5 (1975) 161?166.10.1007/BF01390077 ↗
7. C. Panek and J.J. Kalker, A solution for the narrow rectangular punch. J. Elasticity 7 (1977) 213?218.10.1007/BF00041093 ↗
8. R.J. Atkin, S.C. Cowin and N. Fox, On boundary conditions for polar materials. Z. Angew. Math. Phys. 28 (1977) 1017.10.1007/BF01601669 ↗
9. P.K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science. McGraw-Hill, New York (1981).
10. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, 5th edn. Academic Press, New York (1994).
11. H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vol. 1. McGraw-Hill, New York (1953).
12. V.A. Babeshko, Convolution integral equations of the first kind on a system of segments, arising in elasticity theory and mathematical physics. J. Appl. Math. Mech. 35(1) (1971).10.1016/0021-8928(71)90124-9 ↗
13. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions. Dover, New York (1964).