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arXiv · 2208.09051

Energy Minimizing Configurations for Single-Director Cosserat Shells

Timothy J. Healey·Gokul G. Nair
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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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Timothy J. Healey, Gokul G. Nair. 2022-08-18. Energy Minimizing Configurations for Single-Director Cosserat Shells. https://doi.org/10.1007/s10659-022-09975-4

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