iMechanica - Comments for "Stress of a spatially uniform dislocation density field"
https://imechanica.org/node/22636
Comments for "Stress of a spatially uniform dislocation density field"enAn interesting corollary
https://imechanica.org/comment/29917#comment-29917
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<p><em>In reply to <a href="https://imechanica.org/node/22636">Stress of a spatially uniform dislocation density field</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>It is classically known in continuum mechanics, stated first by the brothers Cosserat [Shield, 1973], that if a second order tensor field on a simply connected domain is at most a curl-free field of rotations, then the field is necessarily constant on the domain. A corollary of the work above is that, at least in dimension 2, this classical result is in fact a special case of a more general situation where the curl of the given rotation field is only known to be at most a constant.</span></p>
<p><span>The classical result can be directly read off from the Rigidity Estimate of Friesecke, James, and Muller (and of course the Generalized Rigidity estimate of Muller, Scardia, Zeppieri (MSZ)). Reading off the present corollary from the Generalized Rigidity Estimate of MSZ would seem to require a little work (Irene Fonseca has shown me such a proof provided the constant in the MSZ Generalized Rigidity Estimate can be shown not to depend on the domain).</span></p>
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</ul>Thu, 06 Dec 2018 21:32:00 +0000Amit Acharyacomment 29917 at https://imechanica.org