Geometry and mechanics of thin growing bilayers

Multiple configuration transitions of soft actuators under single external stimulus

Soft actuators have a wide range of applications in medical instruments, soft robotics, 3D electronics, and deployable structures, where configuration transitions are crucial for their function realization. However, most soft actuators can only morph from the initial configuration directly to the final configuration under a single external stimulus. Herein, we report a novel soft actuator by 3D printing parallel strips with crescent cross-sections onto a thin PDMS film. Multiple configuration transitions are observed when the soft actuator swells in ethyl acetate. Four factors, i.e., the geometric asymmetry of the strips, the fabrication-induced heterogeneity of the film, the differential swelling ratios of the strips and the film, and the geometric parameters of the actuator, are demonstrated to synergistically regulate the multiple configuration transitions of the actuator. Particularly, the underlying mechanisms for the configuration transitions are systematically investigated through experiments and theoretical analysis, and verified via finite element simulation. Benefitting from the multiple configuration transitions, the grasp-release-re-grab function of the actuator is demonstrated under a single stimulus. This work contributes to fundamental understanding of the morphing behaviors and the novel design of soft actuators.

Curvature-driven instabilities in thin active shells

Spontaneous material shape changes, such as swelling, growth or thermal expansion, can be used to trigger dramatic elastic instabilities in thin shells. These instabilities originate in geometric incompatibility between the preferred extrinsic and intrinsic curvature of the shell, which may be modified by active deformations through the thickness and in plane, respectively. Here, we solve the simplest possible model of such instabilities, which assumes the shells are shallow, thin enough to bend but not stretch, and subject to homogeneous preferred curvatures. We consider separately the cases of zero, positive and negative Gauss curvature. We identify two types of supercritical symmetry-breaking instability, in which the shell's principal curvature spontaneously breaks discrete up/down symmetry and continuous planar isotropy. These are then augmented by inversion instabilities, in which the shell jumps subcritically between up/down broken symmetry states and rotation instabilities, in which the curvatures rotate by 90° between states of broken isotropy without release of energy. Each instability has a thickness-independent threshold value for the preferred extrinsic curvature proportional to the square root of Gauss curvature. Finally, we show that the threshold for the isotropy-breaking instability is the same for deep spherical caps, in good agreement with recently published data.

Transient shape morphing of active gel plates: geometry and physics

The control of shape in active structures is a key problem for the realization of smart sensors and actuators, which often draw inspiration from natural systems. In this context, slender structures, such as thin plates, have been studied as a relevant example of shape morphing systems where curvature is generated by in-plane incompatibilities. In particular, in hydrogel plates these incompatibilities can be programmed at fabrication time, such that a target configuration is attained at equilibrium upon swelling or shrinking. While these aspects have been examined in detail, understanding the transient morphing of such active structures deserves further investigation. In this study, we develop a geometrical model for the transient shaping of thin hydrogel plates by extending the theory of non-Euclidean plates. We validate the proposed model using experiments on gel samples that are programmed to reach axisymmetric equilibrium shapes. Interestingly, our experiments show the emergence of non-axisymmetric shapes for early times, as a consequence of boundary layer effects induced by solvent transport. We rationalize these observations using numerical simulations based on a detailed poroelastic model. Overall, this work highlights the limitations of purely geometrical models and the importance of transient, reduced theories for morphing plates that account for the coupled physics driving the evolution of shape. Computational approaches employing these theories will allow to achieve accurate control on the morphing dynamics and ultimately advance 4D printing technologies.

Efficient snap-through of spherical caps by applying a localized curvature stimulus

In bistable actuators and other engineered devices, a homogeneous stimulus (e.g., mechanical, chemical, thermal, or magnetic) is often applied to an entire shell to initiate a snap-through instability. In this work, we demonstrate that restricting the active area to the shell boundary allows for a large reduction in its size, thereby decreasing the energy input required to actuate the shell. To do so, we combine theory with 1D finite element simulations of spherical caps with a non-homogeneous distribution of stimulus-responsive material. We rely on the effective curvature stimulus, i.e., the natural curvature induced by the non-mechanical stimulus, which ensures that our results are entirely stimulus-agnostic. To validate our numerics and demonstrate this generality, we also perform two sets of experiments, wherein we use residual swelling of bilayer silicone elastomers-a process that mimics differential growth-as well as a magneto-elastomer to induce curvatures that cause snap-through. Our results elucidate the underlying mechanics, offering an intuitive route to optimal design for efficient snap-through.

Stretch-Induced Bending of Soft Ribbed Strips

We show that ribbed elastic strips under tension present large spontaneous curvature and may close into tubes. In this single material architectured system, transverse bending results from a bilayer effect induced by Poisson contraction as the textured ribbon is stretched. Surprisingly, the induced curvature may reverse if ribs of different orientations are considered. Slender ribbed structures may also undergo a nontrivial buckling transition. We use analytical calculations to describe the evolution of the morphology of the ribbon and the transitions between the different experimental regimes as a function of material properties, geometrical parameters, and stretching strain. This scale-independent phenomenon may help the manufacturing of tubular textured structures or easily controllable grippers at small scale.

Reprogrammable soft actuation and shape-shifting via tensile jamming

The emerging generation of robots composed of soft materials strives to match biological motor adaptation skills via shape-shifting. Soft robots often harness volumetric expansion directed by strain limiters to deform in complex ways. Traditionally, strain limiters have been inert materials embedded within a system to prescribe a single deformation. Under changing task demands, a fixed deformation mode limits adaptability. Recent technologies for on-demand reprogrammable deformation of soft bodies, including thermally activated variable stiffness materials and jamming systems, presently suffer from long actuation times or introduce unwanted bending stiffness. We present fibers that switch tensile stiffness via jamming of segmented elastic fibrils. When jammed, tensile stiffness increases more than 20× in less than 0.1 s, but bending stiffness increases only 2×. When adhered to an inflating body, jamming fibers locally limit surface tensile strains, unlocking myriad programmable deformations. The proposed jamming technology is scalable, enabling adaptive behaviors in emerging robotic materials that interact with unstructured environments.

Elastic Instabilities Govern the Morphogenesis of the Optic Cup

Because the normal operation of the eye depends on sensitive morphogenetic processes for its eventual shape, developmental flaws can lead to wide-ranging ocular defects. However, the physical processes and mechanisms governing ocular morphogenesis are not well understood. Here, using analytical theory and nonlinear shell finite-element simulations, we show, for optic vesicles experiencing matrix-constrained growth, that elastic instabilities govern the optic cup morphogenesis. By capturing the stress amplification owing to mass increase during growth, we show that the morphogenesis is driven by two elastic instabilities analogous to the snap through in spherical shells, where the second instability is sensitive to the optic cup geometry. In particular, if the optic vesicle is too slender, it will buckle and break axisymmetry, thus, preventing normal development. Our results shed light on the morphogenetic mechanisms governing the formation of a functional biological system and the role of elastic instabilities in the shape selection of soft biological structures.

Nonlinear buckling behavior of a complete spherical shell under uniform external pressure and homogenous natural curvature

In this work, we consider the stability of a spherical shell under combined loading from a uniform external pressure and a homogenous natural curvature. Nonmechanical stimuli, such as one that tends to modify the rest curvature of an elastic body, are prevalent in a wide range of natural and engineered systems, and may occur due to thermal expansion, changes in pH, differential swelling, and differential growth. Here we investigate how the presence of both an evolving natural curvature and an external pressure modifies the stability of a complete spherical shell. We show that due to a mechanical analogy between pressure and curvature, positive natural curvatures can severely destabilize a thin shell, while negative natural curvatures can strengthen the shell against buckling, providing the possibility to design shells that buckle at or above the theoretical limit for pressure alone, i.e., a strengthening factor. These results extend directly from the classical analysis of the stability of shells under pressure, and highlight the important role that nonmechanical stimuli can have on modifying the membrane state of stress in a thin shell.

Computational analysis of hygromorphic self-shaping wood gridshell structures

Bi-layered composites capable of self-shaping are of increasing relevance to science and engineering. They can be made out of anisotropic materials that are responsive to changes in a state variable, e.g. wood, which swells and shrinks by changes in moisture. When extensive bending is desired, such bilayers are usually designed as cross-ply structures. However, the nature of cross-ply laminates tends to prevent changes of the Gaussian curvature so that a plate-like geometry of the composite will be partly restricted from shaping. Therefore, an effective approach for maximizing bending is to keep the composite in a narrow strip configuration so that Gaussian curvature can remain constant during shaping. This represents a fundamental limitation for many applications where self-shaped double-curved structures could be beneficial, e.g. in timber architecture. In this study, we propose to achieve double-curvature by gridshell configurations of narrow self-shaping wood bilayer strips. Using numerical mechanical simulations, we investigate a parametric phase-space of shaping. Our results show that double curvature can be achieved and that the change in Gaussian curvature is dependent on the system's geometry. Furthermore, we discuss a novel architectural application potential in the form of self-erecting timber gridshells.

Printing on liquid elastomers

In recent years the research community has paid significant attention to geometrically engineered materials. These materials derive their unique properties from their structure rather than their chemistry alone. Despite their success in the laboratory, the assembly of such soft functional materials remains an outstanding challenge. Here, we propose a robust fluid-mediated route for the rapid fabrication of soft elastomers architected with liquid inclusions. Our approach consists of depositing water drops at the surface of an immiscible liquid elastomer bath. As the elastomer cures, the drops are encapsulated in the polymer and impart shape and function to the newly formed elastic matrix. Using the framework of fluid mechanics, we show how this type of composite material can be tailored.

Instability of Incompatible Bilayered Soft Tissues and the Role of Interface Conditions

Mechanical stability analysis is instructive in explaining biological processes like morphogenesis, organogenesis, and pathogenesis of soft tissues. Consideration of the layered, residually stressed structure of tissues, requires accounting for the joint effects of interface conditions and layer incompatibility. This paper is concerned with the influence of imposed rate (incremental) interface conditions (RICs) on critical loads in soft tissues, within the context of linear bifurcation analysis. Aiming at simplicity, we analyze a model of bilayered isotropic hyperelastic (neo-Hookean) spherical shells with residual stresses generated by “shrink-fitting” two perfectly bonded layers with radial interfacial incompatibility. This setting allows a comparison between available, seemingly equivalent, interface conditions commonly used in the literature of layered media stability. We analytically determine the circumstances under which the interface conditions are equivalent or not, and numerically demonstrate significant differences between interface conditions with increasing level of layer incompatibility. Differences of more than tenfold in buckling and 30% in inflation instability critical loads are recorded using the different RICs. Contrasting instability characteristics are also revealed using the different RICs in the presence of incompatibility: inflation instability can occur before pressure maximum, and spontaneous instability may be excluded for thin shells. These findings are relevant to the growing body of stability studies of layered and residually stressed tissues. The impact of interface conditions on critical thresholds is significant in studies that use concepts of instability to draw conclusions about the normal development and the pathologies of tissues like arteries, esophagus, airways, and the brain.

Analysis of hygroscopic self-shaping wood at large scale for curved mass timber structures

The growing timber manufacturing industry faces challenges due to increasing geometric complexity of architectural designs. Complex and structurally efficient curved geometries are nowadays easily designed but still involve intensive manufacturing and excessive machining. We propose an efficient form-giving mechanism for large-scale curved mass timber by using bilayered wood structures capable of self-shaping by moisture content changes. The challenge lies in the requirement of profound material knowledge for analysis and prediction of the deformation in function of setup and boundary conditions. Using time- and moisture-dependent mechanical simulations, we demonstrate the contributions of different wood-specific deformation mechanisms on the self-shaping of large-scale elements. Our results outline how to address problems such as shape prediction, sharp moisture gradients, and natural variability in material parameters in light of an efficient industrial manufacturing.

Evolution of critical buckling conditions in imperfect bilayer shells through residual swelling

We propose and investigate a minimal mechanism that makes use of differential swelling to modify the critical buckling conditions of elastic bilayer shells, as measured by the knockdown factor. Our shells contain an engineered defect at the north pole and are made of two layers of different crosslinked polymers that exchange free molecular chains. Depending on the size of the defect and the extent of swelling, we can observe either a decreasing or increasing knockdown factor. FEM simulations are performed using a reduced model for the swelling process to aid us in rationalizing the underlying mechanism, providing a qualitative agreement with experiments. We believe that the working principle of our mechanism can be extended to bimetallic shells undergoing variations in temperature and to shells made of pH-responsive gels, where the change in knockdown factor could be changed dynamically.

Modeling the formation of double rolls from heterogeneously patterned gels

Both stimuli-responsive gels and growing biological tissue can undergo pronounced morphological transitions from two-dimensional (2D) layers into 3D geometries. We derive an analytical model that allows us to quantitatively predict the features of 2D-to-3D shape changes in polymer gels that encompasses different degrees of swelling within the sample. We analyze a particular configuration that emerges from a flat rectangular gel that is divided into two strips (bistrips), where each strip is swollen to a different extent in solution. The final configuration yields double rolls that display a narrow transition layer between two cylinders of constant radii. To characterize the rolls' shapes, we modify the theory of thin incompatible elastic sheets to account for the Flory-Huggins interaction between the gel and the solvent. This modification allows us to derive analytical expressions for the radii, the amplitudes, and the length of the transition layer within a given roll. Our predictions agree quantitatively with available experimental data. In addition, we carry out numerical simulations that account for the complete nonlinear behavior of the gel and show good agreement between the analytical predictions and the numerical results. Our solution sheds light on a stress focusing pattern that forms at the border between two dissimilar soft materials. Moreover, models that provide quantitative predictions on the final morphology in such heterogeneously swelling hydrogels are useful for understanding growth patterns in biology as well as accurately tailoring the structure of gels for various technological applications.

Torque-induced reorientation in active fibre-reinforced materials

We introduce a continuum model for a fibre reinforced material in which the reference orientation of the fibre may evolve with time, under the influence of external stimuli. The model is formulated in the framework of large strain hyperelasticity and the kinematics of the continuum is described by both a position vector and by a remodelling tensor which, in the present context, is an orthogonal tensor representing the fibre reorientation process. By imposing suitable thermodynamical restrictions on the constitutive equation, we obtain an evolution equation of the remodelling tensor governed by the Eshelby torque, whose stationary solutions are studied in absence of any external source terms. It is shown that the fibres reorient themselves in a configuration that minimises the elastic energy and get aligned along a direction that may or may not be of principal strain. The explicit analysis of the Hessian of the strain energy density allows us to discriminate among the stationary solutions, which ones are stable. Examples are given for passive reorientation processes driven by applied strains or external boundary tractions. Applications of the proposed theory to biological tissues, nematic or magneto-electro active elastomers are foreseen.

Buckling of geometrically confined shells

We study the periodic buckling patterns that emerge when elastic shells are subjected to geometric confinement. Residual swelling provides access to range of shapes (saddles, rolled sheets, cylinders, and spherical sections) which vary in their extrinsic and intrinsic curvatures. Our experimental and numerical data show that when these moderately thick structures are radially confined, a single geometric parameter - the ratio of the total shell radius to the amount of unconstrained material - predicts the number of lobes formed. We present a model that interprets this scaling as the competition between radial and circumferential bending. Next, we show that reducing the transverse confinement of saddles causes the lobe number to decrease with a similar scaling analysis. Hence, one geometric parameter captures the wave number through a wide range of radial and transverse confinement, connecting the shell shape to the shape of the boundary that confines it. We expect these results to be relevant for an expanse of shell shapes, and thus applicable to the design of shape-shifting materials and the swelling and growth of soft structures.

Bio-inspired pneumatic shape-morphing elastomers

Shape-morphing structures are at the core of future applications in aeronautics¹, minimally invasive surgery², tissue engineering³ and smart materials⁴. However, current engineering technologies, based on inhomogeneous actuation across the thickness of slender structures, are intrinsically limited to one-directional bending⁵. Here, we describe a strategy where mesostructured elastomer plates undergo fast, controllable and complex shape transformations under applied pressure. Similar to pioneering techniques based on soft hydrogel swelling^6-10, these pneumatic shape-morphing elastomers, termed here as 'baromorphs', are inspired by the morphogenesis of biological structures^11-15. Geometric restrictions are overcome by controlling precisely the local growth rate and direction through a specific network of airways embedded inside the rubber plate. We show how arbitrary three-dimensional shapes can be programmed using an analytic theoretical model, propose a direct geometric solution to the inverse problem, and illustrate the versatility of the technique with a collection of configurations.

Shape and fluctuations of positively curved ribbons

We study the shape and shape fluctuations of incompatible, positively curved ribbons, with a flat reference metric and a spherelike reference curvature. Such incompatible geometry is likely to occur in many self-assembled materials and other experimental systems. Ribbons of this geometry exhibit a sharp transition between a rigid ring and an anomalously soft spring as a function of their width. As a result, the temperature dependence of these ribbons' shape is unique, exhibiting a nonmonotonic dependence of the persistence and Kuhn lengths on the temperature and width. We map the possible configuration phase space and show the existence of three phases: At high temperatures it is the ideal chain phase, where the ribbon is well described by classical models (e.g., wormlike chain model). The second phase, for cold and narrow ribbons, is the plane ergodic phase; a ribbon in this phase might be thought of as made out of segments that gyrate within an oblate spheroid with extreme aspect ratio. The third phase, for cold, wide ribbons, is a direct result of the residual stress caused by the incompatibility, called the random structured phase. A ribbon in this phase behaves on large scales as an ideal chain. However, the segments of this chain are not straight; rather they may have different shapes, mainly helices (both left and right handed) of various pitches.

Helical Structures Mimicking Chiral Seedpod Opening and Tendril Coiling

Helical structures are ubiquitous in natural and engineered systems across multiple length scales. Examples include DNA molecules, plants' tendrils, sea snails' shells, and spiral nanoribbons. Although this symmetry-breaking shape has shown excellent performance in elastic springs or propulsion generation in a low-Reynolds-number environment, a general principle to produce a helical structure with programmable geometry regardless of length scales is still in demand. In recent years, inspired by the chiral opening of Bauhinia variegata's seedpod and the coiling of plant's tendril, researchers have made significant breakthroughs in synthesizing state-of-the-art 3D helical structures through creating intrinsic curvatures in 2D rod-like or ribbon-like precursors. The intrinsic curvature results from the differential response to a variety of external stimuli of functional materials, such as hydrogels, liquid crystal elastomers, and shape memory polymers. In this review, we give a brief overview of the shape transformation mechanisms of these two plant's structures and then review recent progress in the fabrication of biomimetic helical structures that are categorized by the stimuli-responsive materials involved. By providing this survey on important recent advances along with our perspectives, we hope to solicit new inspirations and insights on the development and fabrication of helical structures, as well as the future development of interdisciplinary research at the interface of physics, engineering, and biology.

Droplet-train induced spatiotemporal swelling regimes in elastomers

In this work, we perform a combined experimental and numerical analysis of elastomer swelling dynamics upon impingement of a train of solvent droplets. We use time scale analysis to identify spatiotemporal regimes resulting in distinct boundary conditions that occur based on relative values of the absorption timescale and the droplet train period. We recognize that when either timescale is significantly larger than the other, two cases of quasi-uniform swelling occur. In contrast, when the two timescales are comparable, a variety of temporary geometrical features due to localized swelling are observed. We show that the swelling feature and its temporal evolution depends upon geometric scaling of polymer thickness and width relative to the droplet size. Based on this scaling, we identify six cases of localized swelling and experimentally demonstrate the swelling features for two cases representing limits of thickness and width. A finite element model of local swelling is developed and validated with experimental results for these two cases. The model is subsequently used to explore the swelling behavior in the rest of the identified cases. We show that depending upon the lateral dimension of the sample, swelling can locally exhibit mushroom, mesa, and cap like shapes. These deformations are magnified during the droplet-train impact but dissipate during post-train polymer equilibration. Our results also show that while swelling shape is a function of lateral dimensions of the sample, the extent of swelling increases with the elastomer sample thickness.

Hydrophilic/Hydrophobic Composite Shape-Shifting Structures

Swelling-induced shape transformation has been widely investigated and applied to the design and fabrication of smart polymer devices, such as soft robotics, biomedical devices, and origami patterns. Previous shape-shifting designs using soft hydrogels have several limitations, including relatively small actuation force, slow responsive speed, and relatively complicated fabrication process. In this paper, we develop a novel hydrophilic/hydrophobic composite structure by using photopolymers. The rubbery nature of the materials used in this composite provides desirable actuation speed and actuation force. The photocurable polymer system could be easily patterned by using the digital light processing technique. Experiments and theoretical analysis were conducted to study the actuation process. We also fabricated several three-dimensional water-responsive shape-shifting structures, including structures with sequential actuation behavior. Finally, the directional bending behavior of the hydrophilic/hydrophobic bilayer plate was investigated.

Curvature-Induced Instabilities of Shells

Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of spontaneous curvature and geometric frustration in curved shells remains poorly understood. Via a combination of precision experiments on elastomeric spherical shells, simulations, and theory, we show how a spontaneous curvature induces a rotational symmetry-breaking buckling as well as a snapping instability reminiscent of the Venus fly trap closure mechanism. The instabilities, and their dependence on geometry, are rationalized by reducing the spontaneous curvature to an effective mechanical load. This formulation reveals a combined pressurelike term in the bulk and a torquelike term in the boundary, allowing scaling predictions for the instabilities that are in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced subcritical buckling in closed shells. We determine the critical buckling curvature via a linear stability analysis that accounts for the combination of residual membrane and bending stresses. The prominent role of geometry in our findings suggests the applicability of the results over a wide range of scales.

Growth patterns for shape-shifting elastic bilayers

Inspired by the differential-growth-driven morphogenesis of leaves, flowers, and other tissues, there is increasing interest in artificial analogs of these shape-shifting thin sheets made of active materials that respond to environmental stimuli such as heat, light, and humidity. But how can we determine the growth patterns to achieve a given shape from another shape? We solve this geometric inverse problem of determining the growth factors and directions (the metric tensors) for a given isotropic elastic bilayer to grow into a target shape by posing and solving an elastic energy minimization problem. A mathematical equivalence between bilayers and curved monolayers simplifies the inverse problem considerably by providing algebraic expressions for the growth metric tensors in terms of those of the final shape. This approach also allows us to prove that we can grow any target surface from any reference surface using orthotropically growing bilayers. We demonstrate this by numerically simulating the growth of a flat sheet into a face, a cylindrical sheet into a flower, and a flat sheet into a complex canyon-like structure.

Multi-parameter actuation of a neutrally stable shell: a flexible gear-less motor

We have designed and tested experimentally a morphing structure consisting of a neutrally stable thin cylindrical shell driven by a multi-parameter piezoelectric actuation. The shell is obtained by plastically deforming an initially flat copper disc, so as to induce large isotropic and almost uniform inelastic curvatures. Following the plastic deformation, in a perfectly isotropic system, the shell is theoretically neutrally stable, having a continuous set of stable cylindrical shapes corresponding to the rotation of the axis of maximal curvature. Small imperfections render the actual structure bistable, giving preferred orientations. A three-parameter piezoelectric actuation, exerted through micro-fibre-composite actuators, allows us to add a small perturbation to the plastic inelastic curvature and to control the direction of maximal curvature. This actuation law is designed through a geometrical analogy based on a fully nonlinear inextensible uniform-curvature shell model. We report on the fabrication, identification and experimental testing of a prototype and demonstrate the effectiveness of the piezoelectric actuators in controlling its shape. The resulting motion is an apparent rotation of the shell, controlled by the voltages as in a 'gear-less motor', which is, in reality, a precession of the axis of principal curvature.

Curvature-driven morphing of non-Euclidean shells

We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive an effective model that reduces a three-dimensional stimulus to the natural fundamental forms of the mid-surface of the structure, incorporating expansion, or growth, in the thickness. Then, we apply the model to a variety of thin bodies, from flat plates to spherical shells, obtaining excellent agreement between theory and numerics. We show how cylinders and cones can either bend more or unroll, and eventually snap and rotate. We also study the nearly isometric deformations of a spherical shell and describe how this shape change is ruled by the geometry of a spindle. As the derived results stem from a purely geometrical model, they are general and scalable.

Programmable shape transformation of elastic spherical domes

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.