iMechanica - mechanics of defects
https://imechanica.org/taxonomy/term/9755
enNon-Metricity and the Nonlinear Mechanics of Distributed Point Defects
https://imechanica.org/node/16525
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/2356">differential geometry</a></div><div class="field-item odd"><a href="/taxonomy/term/4582">Geometric mechanics</a></div><div class="field-item even"><a href="/taxonomy/term/9754">Point defects</a></div><div class="field-item odd"><a href="/taxonomy/term/9755">mechanics of defects</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>We discuss the relevance of non-metricity in a metric-affine manifold (a manifold equipped with a connection and a metric) and the nonlinear mechanics of distributed point defects. We describe a geometric framework in which one can calculate analytically the residual stress field of nonlinear elastic solids with distributed point defects. In particular, we use Cartan's machinery of moving frames and construct the material manifold of a finite ball with a spherically-symmetric distribution of point defects. We then calculate the residual stress field when the ball is made of an arbitrary incompressible isotropic solid. We will show that an isotropic distribution of point defects cannot be represented by a distribution of purely dilatational eigenstrains. However, it can be represented by a distribution of radial eigenstrains. We also discuss an analogy between the residual stress field and the gravitational field of a spherical mass.</p>
</div></div></div>Thu, 01 May 2014 16:09:12 +0000Arash_Yavari16525 at https://imechanica.orghttps://imechanica.org/node/16525#commentshttps://imechanica.org/crss/node/16525