Growth patterns for shape-shifting elastic bilayers
Abstract
Many biological forms, such as leaves, flowers, and faces, are shaped by complex growth patterns. How can we prescribe the rules of growth on a simple surface so that it will morph into a flower or a face? Here, we solve this inverse problem of designing the growth patterns for an anisotropically growing elastic bilayer structure and prove that it can be used to achieve any target surface shape from any reference shape. We demonstrate the applicability of this result via the computational design of growth patterns for animal, vegetable, and mineral surfaces—a face, a flower, and a canyon. Our solution provides algorithms for engineering complex functional shapes in tissues, and actuation systems in soft robotics, and elsewhere.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Oct 16, 2017
- Source ID
- 10.1073/pnas.1709025114
Entities
People
- Etienne Vouga
- Lakshminarayanan Mahadevan
- Wim M van Rees
Organizations
- Army Research Office
- Harvard University
- National Science Foundation
- University of Texas at Austin