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# Contact Mechanics .

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Diagram. What is Contact Mechanics?The two distinctive sort of contacts.Boussinesq and Cerruti Potential FunctionsThe particular instance of an Applied Normal ForceHertz Equations-Derivation, AssumptionsRigid Sphere Contacting a Deformable PlateDeformable Sphere Contacting a Rigid Plate. What is Contact Mechanics?.
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﻿Contact Mechanics Maria Persson Gulda Kathleen DiSanto

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Outline What is Contact Mechanics? The two diverse sort of contacts. Boussinesq and Cerruti Potential Functions The particular instance of an Applied Normal Force Hertz Equations-Derivation, Assumptions Rigid Sphere Contacting a Deformable Plate Deformable Sphere Contacting a Rigid Plate

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What is Contact Mechanics? "[The hypothesis of contact mechanics] is worried with the anxieties and twisting which emerge when the surfaces of two strong bodies are brought into contact." Professor Johnsson

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Two sorts of contact Conforming contacts The two surfaces fit precisely or firmly together without distortion Non-accommodating contact The surfaces, or one of the two surfaces, misshapes when there is a contact region in the middle of them.

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Derivation: Boussinesq and Cerruti Potential Functions Here are the potential capacities: Each fulfill Laplace\'s condition:

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Special Case: Applied Pressure Only The potential capacities are lessened as takes after: Displacement conditions: By Hooke\'s Law, the anxieties are:

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Concentrated Normal Force on an Elastic Half Space The removals are: The worries in polar directions:

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Concentrated Force Cont. Presently taking a gander at the surface, z=0 The relocations in polar directions get to be: For a general weight dispersion, the removal for any surface point in S, by Green\'s capacity strategy, becomes:

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Hertz Pressure The Pressure appropriation is: Equation for deciding surface uprooting: The Hertz dislodging condition: where an is the span of the contact region

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Hertz Theory of Elastic Contact Assumptions: The radii of ebb and flow of the reaching bodies are huge contrasted and the range of the hover of contact. The measurements of every body are expansive contrasted with the sweep of the hover of contact. The reaching bodies are in frictionless contact. The surfaces in contact are persistent and nonconforming.

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Examples Focus on two illustrations: Rigid round indenter pushing to deformable level surface. Deformable circle reaching unbending plate. (2) (1)

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Equations to be Used – where R\' is the range of the inflexible circle and R S is the sweep of the deformable plate (2) – where δ is the vertical separation the point where the heap is connected moves and an is the contact territory span dictated by the condition: (3) – h is the first separation between a point on the unbending circle and the deformable plate before load application. (4) – These are the conditions of uprooting determined beforehand (5) – This expresses the interpretation of the purpose of load application breaks even with the surface removal of the plate and circle in addition to the first separation between the surfaces.

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Rigid Sphere Contacting Deformable Flat Surface with Abaqus Theoretical Contact Radius: 11.995 mm Abaqus Contact Radius: 11.6 mm Error: 3%

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Deformable Sphere Contacting Rigid Plate with Abaqus Theoretical Contact Radius: 9.288 mm Abaqus Contact Radius: 8.5 mm Error: 6%

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Conclusion Contact issues by and large are extremely convoluted to demonstrate numerically and hypothetically Other elements Friction - unpleasant surfaces Blunt edges, sharp corners Sliding and moving contact Dynamic effect

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A Special Thank You To: Dr. Ashkan Vaziri Professor James Rice

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References Johnson, K. L. Contact Mechanics, Cambridge: Cambridge University Press; 1985 Fisher-Cripps, A. C. The Hertzian contact surface. J. Materials Science. 1999;34:129-137 Kogut, L., Etsion, I. Versatile Plastic Contact Analysis of a Sphere and a Rigid Flat. J. of Applied Mechanics. 2002;69:657-662 Johnson, K. L., Greenwood, J. A. An Adhesion Map for the contact of flexible Spheres. J. of Colloid and Interface Science . 1997;192:326-333 Barber, J. R.,Clavarella, M. Contact mechanics. Bury. J. of Solids and Structures. 2000;37:29-43

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