Buckling of geometrically confined shells
Lucia Stein-Montalvo, Paul Costa, Matteo Pezzulla and Douglas P. Holmes
Soft Matter, 15(6), 1215-1222, (2019).
Abstract: 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.
Multistable kirigami for tunable architected materials
Yi Yang, Marcelo A. Dias, and Douglas P. Holmes
Physical Review Materials, 2, 110601(R)
Abstract: In nature, materials such as ferroelastics and multiferroics can switch their microstructure in response to external stimuli, and this reconfiguration causes a simultaneous modulation of their material properties. Rapid prototyping technologies have enabled origami and kirigami-inspired architected materials to provide a means for designing shape-shifting structures, and here we show how multistable structures inspired by kirigami provide novel design criteria for preparing mechanical metamaterials with tunable properties. By changing the geometry of kirigami unit cells, we obtain multistable kirigami lattice structures endowed with a bistable snap-through mechanism. We demonstrate the precise control of material stiffness, along with the ability to tune this property in situ by locally and reversibly switching the unit cell configurations. We anticipate these mechanical metamaterials will provide a platform to achieve in situ tunable electrical, optical, and mechanical properties for a variety of applications in multifunctional materials, two-dimensional materials, and soft robotics.
Snapping of bistable, prestressed cylindrical shells
Xin Jiang, Matteo Pezzulla, Huiqi Shao, Tushar K. Ghosh, and Douglas P. Holmes,
Europhysics Letters (EPL), 122, 6, (2018).
Bistable shells can reversibly change between two stable configurations with very little energetic input. Understanding what governs the shape and snap-through criteria of these structures is crucial for designing devices that utilize instability for functionality. Bistable cylindrical shells fabricated by stretching and bonding multiple layers of elastic plates will contain residual stress that will impact the shell’s shape and the magnitude of stimulus necessary to induce snapping. Using the framework of incompatible elasticity, we first predict the mean curvature of a nearly cylindrical shell formed by arbitrarily prestretching one layer of a bilayer plate with respect to another. Then, beginning with a residually stressed cylinder, we determine the amount of the stimuli needed to trigger the snapping between two configurations through a combination of numerical simulations and theory. We demonstrate the role of prestress on the snap-through criteria, and highlight the important role that the Gaussian curvature in the boundary layer of the shell plays in dictating shell stability.
Bioinspired Electrically Activated Soft Bistable Actuators
Huiqi Shao, Shuzhen Wei, Xin Jiang, Douglas P. Holmes, and Tushar K. Ghosh
Advanced Functional Materials, 18029999, (2018).
Movement and morphing in biological systems provide insights into the materials and mechanisms that may enable the development of advanced engineering structures. The nastic motion of plants in response to environmental stimuli, e.g., the rapid closure of the Venus flytrap’s leaves, utilizes snap‐through instabilities originating from anisotropic deformation of plant tissues. In contrast, ballistic tongue projection of chameleon is attributed to direct mechanical energy transformation by stretching elastic tissues in advance of rapid projection to achieve higher speed and power output. Here, a bioinspired trilayered bistable all‐polymer laminate containing dielectric elastomers (DEs) is reported, which double as both structural and active materials. It is demonstrated that the prestress and laminating strategy induces tunable bistability, while the electromechanical response of the DE film enables reversible shape transition and morphing. Electrical actuation of bistable structures obviates the need for continuous application of electric field to sustain their transformed state. The experimental results are qualitatively consistent with our theoretical analyses of prestrain‐dependent shape and bistability.
Static Bistability of Spherical Caps
Matteo Taffetani, Xin Jiang, Douglas P. Holmes, and Dominic Vella
Proceedings of the Royal Socitey A, 474(2213), (2018).
Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two ‘self-equilibrated’ states, one natural and the other inside out (or ‘everted’). Though this is familiar from everyday life—an umbrella is remarkably stable, yet a contact lens can be easily turned inside out the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite-element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more ‘robust’ to snap-through. Our work sheds new light on the robustness of the ‘mirror buckling’ symmetry of spherical shell caps.
The soft matter blog “Softbites” recently highlighted our work on elastogranularity. The blog post was written by Adam Fortais, and nicely highlights the connection between elastogranular interactions and root growth.
Elastogranular Mechanics: Buckling, Jamming, and Structure Formation
David J. Schunter, Jr., Martin Brandenbourger, Sophia Perriseau, and Douglas P. Holmes,
Physical Review Letters, 120, 078002, (2018).
Confinement of a slender body into a granular array induces stress localization in the geometrically nonlinear structure, and jamming, reordering, and vertical dislodging of the surrounding granular medium. By varying the initial packing density of grains and the length of a confined elastica, we identify the critical length necessary to induce jamming, and demonstrate how folds couple with the granular medium to localize along grain boundaries. Above the jamming threshold, the characteristic length of elastica deformation is shown to diverge in a manner that is coupled with the motion and rearrangement of the grains, suggesting the ordering of the granular array governs the deformation of the slender structure. However, overconfinement of the elastica will vertically dislodge grains, a form of stress relaxation in the granular medium that illustrates the intricate coupling in elastogranular interactions.
Curvature-Induced Instabilities of Shells
Matteo Pezzulla, Norbert Stoop, Mark P. Steranka, Abdikhalaq J. Bade, and Douglas P. Holmes, Physical Review Letters, 120, 048002, (2018).
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.
Extended lubrication theory: improved estimates of flow in channels with variable geometry
Behrouz Tavakol, Guillaume Froehlicher, Douglas P. Holmes, Howard A. Stone, Proceedings of the Royal Society A, 0234, (2017).
Abstract: Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions, while numerical results are in very good agreement with the higher-order analytical results. We show that the extended lubrication theory is a robust tool for an accurate estimate of pressure drop in channels with shape changes on the order of the channel height, accounting for both smooth and sharp changes in geometry.
Marcelo A. Dias, Michael P. McCarron, Daniel Rayneau-Kirkhope, Paul Z. Hanakata, David K. Campbell, Harold S. Park and Douglas P. Holmes, Soft Matter, 13, 9087-9802, (2017).
Abstract: Thin elastic sheets bend easily and, if they are patterned with cuts, can deform in sophisticated ways. Here we show that carefully tuning the location and arrangement of cuts within thin sheets enables the design of mechanical actuators that scale down to atomically-thin 2D materials. We first show that by understanding the mechanics of a single non-propagating crack in a sheet, we can generate four fundamental forms of linear actuation: roll, pitch, yaw, and lift. Our analytical model shows that these deformations are only weakly dependent on thickness, which we confirm with experiments on centimeter-scale objects and molecular dynamics simulations of graphene and MoS2 nanoscale sheets. We show how the interactions between non-propagating cracks can enable either lift or rotation, and we use a combination of experiments, theory, continuum computational analysis, and molecular dynamics simulations to provide mechanistic insights into the geometric and topological design of kirigami actuators.