Energy Minimizing Configurations for Single-Director Cosserat Shells

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 condition...

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Bibliographic Details
Published inJournal of elasticity Vol. 154; no. 1-4; pp. 569 - 578
Main Authors Healey, Timothy J., Nair, Gokul G.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.11.2023
Springer Nature B.V
Subjects
Biomechanics
Classical and Continuum Physics
Classical Mechanics
Configurations
Engineering
Internal energy
Materials Science
Mathematical Applications in the Physical Sciences
Theoretical and Applied Mechanics
49K20
Plates and Shells
35D99
Energy minimization
Nonlinear elasticity
74B20
Polyconvexity
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ISSN0374-3535
1573-2681
DOI10.1007/s10659-022-09975-4

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Summary: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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ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-022-09975-4