LDG approximation of large deformations of prestrained plates

•Formal derivation of prestrained hyper-elastic plates model.•Novel reformulation amenable to variational approximation methods.•Novel finite element methods based on reconstructed Hessians.•Insightful numerical experiments. A reduced model for large deformations of prestrained plates consists of mi...

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Published inJournal of computational physics Vol. 448; p. 110719
Main Authors Bonito, Andrea, Guignard, Diane, Nochetto, Ricardo H., Yang, Shuo
Format Journal Article
LanguageEnglish
Published Cambridge Elsevier Inc 01.01.2022
Elsevier Science Ltd
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ISSN0021-9991
1090-2716
DOI10.1016/j.jcp.2021.110719

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Summary:•Formal derivation of prestrained hyper-elastic plates model.•Novel reformulation amenable to variational approximation methods.•Novel finite element methods based on reconstructed Hessians.•Insightful numerical experiments. A reduced model for large deformations of prestrained plates consists of minimizing a second order bending energy subject to a nonconvex metric constraint. The former involves the second fundamental form of the middle plate and the latter is a restriction on its first fundamental form. We discuss a formal derivation of this reduced model along with an equivalent formulation that makes it amenable computationally. We propose a local discontinuous Galerkin (LDG) finite element approach that hinges on the notion of reconstructed Hessian. We design discrete gradient flows to minimize the ensuing nonconvex problem and to find a suitable initial deformation. We present several insightful numerical experiments, some of practical interest, and assess various computational aspects of the approximation process.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2021.110719