Curved geometries from planar director fields - Solving the two-dimensional inverse problem
| Autor: | Efi Efrati, Itay Griniasty, Hillel Aharoni |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Surface (mathematics)
Physics Integrable system Field (physics) Differential equation Mathematical analysis General Physics and Astronomy Inverse FOS: Physical sciences Condensed Matter - Soft Condensed Matter Inverse problem 16. Peace & justice 01 natural sciences Condensed Matter::Soft Condensed Matter Planar Orientation (geometry) 0103 physical sciences Soft Condensed Matter (cond-mat.soft) 010306 general physics |
| DOI: | 10.48550/arxiv.1902.09902 |
| Popis: | Thin nematic elastomers, composite hydrogels and plant tissues are among many systems that display uniform anisotropic deformation upon external actuation. In these materials, the spatial orientation variation of a local director field induces intricate global shape changes. Despite extensive recent efforts, to date, there is no general solution to the inverse design problem: how to design a director field that deforms exactly into a desired surface geometry upon actuation, or whether such a field exists. In this work, we phrase this inverse problem as a hyperbolic system of differential equations. We prove that the inverse problem is locally integrable, provide an algorithm for its integration, and derive bounds on global solutions. We classify the set of director fields that deform into a given surface, thus paving the way to finding optimized fields. Comment: 10 pages, 6 figures |
| Databáze: | OpenAIRE |
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