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Energy Minimizing Configurations for Single-Director Cosserat Shells

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Abstract

We consider a class of single-director Cosserat shell models accounting for both curvature and finite mid-plane strains. We assume a polyconvexity condition for the stored-energy function that reduces to a physically correct membrane model in the absence of bending. With appropriate growth conditions, we establish the existence of energy minimizers. The local orientation of a minimizing configuration is maintained via the blowup of the stored energy as a version of the local volume ratio approaches zero. Finally, we specialize our results to three constrained versions of the theory commonly employed in the subject.

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Acknowledgements

This work was supported in part by the National Science Foundation through grant DMS-2006586, which is gratefully acknowledged.

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TJH and GGN contributed equally to the manuscript.

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Correspondence to Gokul G. Nair.

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Dedicated to Roger Fosdick on the occasion of his 85th Birthday

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Healey, T.J., Nair, G.G. Energy Minimizing Configurations for Single-Director Cosserat Shells. J Elast 154, 569–578 (2023). https://doi.org/10.1007/s10659-022-09975-4

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  • DOI: https://doi.org/10.1007/s10659-022-09975-4

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