Elastic theory of unconstrained non-Euclidean plates
By Efi Efrati, Eran Sharon, Raz Kupferman. 2008
369 citations recorded by the source corpus.
Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the absence of external forces. In this work we present a mathematical framework for such bodies in terms of a covariant theory of linear elasticity, valid for large displacements. We propose the concept of non-Euclidean plates to approximate many naturally formed thin elastic structures. We derive a thin plate theory, which is a generalization of existing linear plate theories, valid for large displacements but small strains, and arbitrary intrinsic geometry. We study a particular example of a hemispherical plate. We show the occurrence of a spontaneous buckling transition from a stretching dominated configuration to bending dominated configurations, under variation of the plate thickness.
Subfields: Cell Biology, Civil and Structural Engineering, Mechanical Engineering
View Paper: https://www.semanticscholar.org/paper/fd3ba226adcb3ee33db71d8c6049c46cb0a7f939
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Citations in the corpus
- Shape control of active surfaces inspired by the movement of euglenids (2014, methodology): “For this purpose, we adopt the elastic theory of non-Euclidean plates (Efrati et al., 2009), and find the shapes resulting from minimizing the discrepancy between the actual and the target metrics, in the presence of a small bending energy.”