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arXiv · 1410.4225

Existence theorem for geometrically nonlinear Cosserat micropolar model under uniform convexity requirements

Patrizio Neff·Mircea Bîrsan·Frank Osterbrink
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Abstract

We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium problem as a minimization problem. Applying the direct methods of the calculus of variations we show the existence of minimizers. We present a clear proof based on the coercivity of the elastically stored energy density and on the weak lower semi-continuity of the total energy functional. Use is made of the dislocation density tensor $\bar{\boldsymbol{K}}=\bar{\boldsymbol{R}}^T\,\mathrm{Curl}\,\bar{\boldsymbol{R}}$ as a suitable Cosserat curvature measure.

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Patrizio Neff, Mircea Bîrsan, Frank Osterbrink. 2014-12-15. Existence theorem for geometrically nonlinear Cosserat micropolar model under uniform convexity requirements. https://arxiv.org/abs/1410.4225

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