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Author ORCID Identifier



Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program

Polymer Science and Engineering

Year Degree Awarded


Month Degree Awarded


First Advisor

Ryan Hayward


Non-Euclidean shells are ubiquitous in both natural and man-made systems, yet fabrication at smaller length-scales (nanometer to micrometer) and the underlying mechanical behavior of these geometries is not well understood. In this dissertation, we develop a framework for improvements in fabrication and control over deformation pathways of non-Euclidean elastic shells.

For programming a target non-Euclidean geometry, we study the non-uniform growth induced buckling in flat sheets. To deepen our understanding of this powerful mechanism, we present an experimental verification of its mathematical equivalence with a mechanism involving topological defects. We establish a framework for correlating topological defect-induced buckling, realized through a simple cut-and-glue construction, with growth induced buckling realized through non-uniform growth of patterned 2D hydrogel sheets. Validating the obtained mathematical results, we demonstrate fabrication of a cylindrical and conical dipole geometry through both mechanisms under consideration. In addition, upon applying a similar treatment on tetrahedron geometry we realize the limitations of growth-induced buckling mechanism for programming 3D geometry, and find that optimizing for pattern resolution and swelling range can lead to a higher fidelity in target geometries.

Next, we turn towards the interplay between geometry and mechanics in non-Euclidean shells, to harness multi-stability between different geometric configurations. Under this theme, we study deformation of arbitrarily curved surfaces along pre-defined creases (curves with local weakening) finding that the continuity of this deformation can be predicted through a simple consideration of the curvature of the crease. We establish that simple geometric control over the crease curvature can be used to program on-demand snap-through instabilities between bi-stable states of developable, elliptic and hyperbolic surfaces. Using experiments, FEA and theoretical analysis of bending and stretching energies involved while indenting a hemispherical shell, we establish the geometric phase space in which the isometric state of a creased sphere is stable.

Finally, we extend this notion by considering the ability to program multiple stable states in a tiled conical geometry, commonly found in bendable drinking straws (bendy straws) and other similar structures. These corrugated structures exhibit stability in axial (resulting in change in length), non-axial (change in ‘bent’ angle) and azimuthal direction (change in azimuthal angle) imparting a desirable high-degree of freedom in possible configurations. By analyzing the stability behavior of elastic double conical frusta shells, we study the necessary conditions for programming multi-stability, and find that axial stability depends on geometrical parameters. Interestingly, we conclude that a stable non-axial state requires a combination of appropriate geometry and presence of a pre-stress in azimuthal direction. The controlled multi-stability opens pathways toward a truly re-configurable shape programmable system, useful for manipulators and actuators in soft-robotics