Elastic Deformation

Elastic Deformation

Revision for “Elastic Deformation” created on February 16, 2017 @ 14:14:24 [Autosave]

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Elastic Deformation
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<h2>Definition</h2> Elastic deformation is a change of the shape of the body as a reaction to applied stress. This deformation is only temporary and once the stress is released, the undeformed shape of the body is restored, as shown in the figure below. In tribology, elastic deformation largely affects <a href="http://www.tribonet.org/wiki/elastohydrodynamic-lubrication-ehl/" target="_blank">elastohydrodynamic film thickness</a> build up, real contact area, etc. A problem of determination of elastic deformation in various scenarios is considered in the classical <a href="https://docs.google.com/file/d/0Bw8MfqmgWLS4NTlFNF9VZzBZdWs/view" target="_blank">Elasticity Theory book by Timoshenko and Goodier</a> [1]. <img class="aligncenter wp-image-1936 size-large" src="http://www.tribonet.org/wp-content/uploads/2017/02/Elastic-Deformation-300x234.jpg" alt="Elastic Deformation" width="300" height="234" data-wp-pid="1936" /> <h2>Application</h2> In the field of tribology, the most commonly studied configuration of contact is the contact of a sphere or a cylinder with a flat (the contact of two spheres or two cylinders can be reduced to the contact on flat). In this case, a half-space approximation is applicable and the full system of Elasticity Theory equations can be solved analytically to link the elastic deflection to the applied pressure [1]. The resultant equation is given in integral form: <p style="text-align: justify;">[math] \begin{eqnarray} \label{complete_sys1}</p> <p style="text-align: justify;">h_e(x,y) = \frac{2\pi}{E'} \int\int \frac{p(x',y')}{\sqrt{(x-x')^2+(y-y')^2}}dx'dy' \\</p> <p style="text-align: justify;">\end{eqnarray} [/math]</p> <p style="text-align: justify;">This equation is typically used in EHL problems, but also in contact analysis, friction and wear simulation. Further information regarding the application of the equation can be found in the <a href="http://link.springer.com/article/10.1007/s11249-015-0536-z">reference</a> [2].</p> &nbsp; [1] <a href="https://docs.google.com/file/d/0Bw8MfqmgWLS4NTlFNF9VZzBZdWs/view">Theory of Elasticity</a>, Timoshenko, S.P., Goodier, J.N., 1970. <p class="ArticleTitle" lang="en">[2] On a Model for the Prediction of the Friction Coefficient in Mixed Lubrication Based on a Load-Sharing Concept with Measured Surface  Roughness, <span class="authors__name">Aydar Akchurin,</span><span class="authors__name">Rob Bosman, </span><span class="authors__name">Piet M. Lugt, </span><span class="authors__name">Mark van Drogen.</span></p> &nbsp; <span style="border-radius: 2px; text-indent: 20px; width: auto; padding: 0px 4px 0px 0px; text-align: center; font: bold 11px/20px 'Helvetica Neue',Helvetica,sans-serif; color: #ffffff; background: no-repeat scroll 3px 50% / 14px 14px #bd081c; position: absolute; opacity: 1; z-index: 8675309; display: none; cursor: pointer; top: 208px; left: 368px;">Save</span>
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