Programmable shape transformation of elastic spherical domes

Abstract

We investigate mismatch strain driven programmable shape transformation of spherical domes and report the effects of different geometric and structural characteristics on dome behavior in response to applied mismatch strain. We envision a bilayer dome design where the differential swelling of the inner layer with respect to the passive outer layer in response to changes in dome surroundings (such as the introduction of an organic solvent) introduces mismatch strain within the bilayer system and causes dome shape transformation. Finite element analysis reveals that, in addition to snap-through, spherical domes undergo bifurcation buckling and eventually gradual bending to morph into cylinders with increasing mismatch strain. Besides demonstrating how the snap-through energy barrier depends on the spherical dome shape, our analysis identifies three distinct groups of dome geometries based on their mismatch strain-transformed configuration relationships. Our experiments with polymer-based elastic bilayer domes that exhibit differential swelling in organic solvents qualitatively confirm the finite element predictions. We establish that, in addition to externally applied stimuli (mismatch strain), bilayer spherical dome morphing can be tuned and hence programmed through its geometry and structural characteristics. Incorporation of an elastic instability mechanism such as snap-through within the framework of stimuli-responsive functional devices can improve their response time which is otherwise controlled by diffusion. Hence, our proposed design guidelines can be used to realize deployable, multi-functional, reconfigurable, and therefore, adaptive structures responsive to a diverse set of stimuli across multiple length scales.

Curvature-Induced Instabilities of Shells

“…Explicitly, the triple point is deter-mined from −κ s + 2/R = κ b , which givesθ c = 3.85, in agreement with experiments (θ c = 3.95 ± 0.26). Consequently, shells snap into a rotationally symmetric phase only ifθ s <θ <θ c , whereas forθ >θ c , shells immediately snap into an everted state of broken rotational symmetry (blue region; thin shells are unlikely to snap into cylindrical shapes [28]. However, we would expect the deformed shells have a small, nonzero curvature along one principal direction, corresponding to a near isometric deformation with minimum energy).…”

Elasticity and stability of shape-shifting structures

“…A recent review on this topic by Hu et al will hopefully provide a nice compliment to the following discussion [83]. There have been demonstrations of actuating snapthrough instabilities for just about every conceivable mechanical and non-mechanical stimulus, including temperature [84], light [85], acoustic excitation [86,87], elastomer or gel swelling [88,89,90,12], magnetic fields [91,92], fluid flow [93], surface tension or elastocapillarity [94], and electrical current with materials that include from ceramic (piezoelectric) [95,96], metallic (electrostatic) [97,98], and rubber (dielectric elastomers) [99,100,23,101]. Laminated composites of epoxy and carbon fiber or fiber glass may exhibit bistability or multistability while thermally curing [102,103,104,105].…”

Kirigami‐Inspired Self‐Assembly of 3D Structures

“…The commercially available finite element analysis package ABAQUS[71] for understanding the mechanics of the stimulus‐responsive shape transformation behavior of Kirigami‐cut bilayers was used. Following an already established protocol,[40,43,72–74] the mismatch strain‐driven bilayer morphing was modeled as an equivalent thermal expansion problem where one layer expands with respect to the other in response to a hypothetical temperature. In our computations, 4‐node general purpose shell elements with through‐thickness variation in material properties (the element size was determined from separate mesh refinement studies) and appropriate boundary conditions were used.…”

“…It is worth mentioning that, although the self‐folding behavior of bilayers is often thought to be one involving simple unidirectional bending,[39] the nature of bilayer morphing strongly depends on its geometric parameters and structural instabilities. [40–42] We rely on a finite element modeling (FEM)[43–47] guided approach as the FE models enable us to understand the mechanics behind the bilayer shape transformation behavior and the relationships between initial geometries, applied stimulus, and transformed shapes. We also fabricate millimeter‐scaled hinge‐less poly(dimethylsiloxane) (PDMS) bilayers with different cross‐linking densities (Figure S1, Supporting Information) and transform them into complex 3D configurations such as those representing letters from the Roman alphabet, quasi‐axisymmetric flower petal‐like structures, and open/ closed polyhedral architectures with varying number of faces (through solvent‐induced swelling experiments).…”