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Many complex wetting behaviors of fibrous materials are rooted in the behaviors of individual droplets attached to pairs of fibers. Here, we study the splitting of a droplet held between the tips of two cylindrical fibers. We discover a sharp transition between two post-rupture states, navigated by changing the angle between the rods, in agreement with our bifurcation analysis. Depinning of the bridge contact line can lead to a much larger asymmetry between the volume of liquid left on each rod. This second scenario enables the near-complete transfer of an aqueous glycerol droplet between two identical vinylpolysiloxane fibers. We leverage this response in a device that uses a ruck to pass a droplet along a train of fibers, a proof-of-concept for the geometric control of droplets on deformable, architected surfaces. 

Topology is an important determinant of the behavior of a great number of condensed-matter systems, but until recently has played a minor role in elasticity. We develop a theory for the deformations of a class of twisted non-Euclidean sheets which have a symmetry based on the celebrated Bonnet isometry. We show that non-orientability is an obstruction to realizing the symmetry globally, and induces a geometric phase that captures a memory analogous to a previously identified one in 2D metamaterials. However, we show that orientable ribbons can also obstruct realizing the symmetry globally. This new obstruction is mediated by how the unit normal vector winds around the centerline of the ribbon, and provides conditions for constructing soft modes of deformation compatible with the topology of multiply-twisted connected ribbons. 

Nanoparticles, such as viruses, can enter cells via endocytosis, a process by which the cell membrane wraps around them. The role of nanoparticle size and shape on endocytosis has been well studied, but the biophysical details of how extracellular proteins on the cell membrane surface mediate uptake are less clear. Motivated by recent discoveries regarding extracellular vimentin in viral and bacterial uptake and the structure of coronaviruses, we construct a computational model with a cell-like and virus-like construct containing filamentous protein structures protruding from their surfaces. We study the impact of these additional degrees of freedom on viral wrapping. The cell surface is modeled as a deformable sheet with bending rigidity, and extracellular vimentin as semiflexible polymers, or extracellular components (ECC), placed randomly on the sheet. The virus is modeled as a deformable shell that also has explicit, freely rotating spike filaments on its surface. Our results indicate that cells with optimally populated filaments are more susceptible to infection as they take up the virus more quickly and utilize a relatively smaller area of the cell surface. At optimal ECC density, the cell surface forms a fold around the virus, which is faster and more efficient at wrapping than localized crumples. Additionally, cell surface bending rigidity aids in the generation of folds by increasing force transmission across the surface. Changing other mechanical parameters, such as the stretching stiffness of filamentous ECC or virus spikes, can result in localized crumple formation on the cell surface. We conclude with the implications of our study on the evolutionary pressures of virus-like particles, with a particular focus on the cellular microenvironment. Published by the American Physical Society2025 

A design for a metamaterial with tunable stiffness is introduced. The material can be switched from floppy to rigid by changing the lengths of the constituent beams, which is demonstrated using a temperature-responsive hydrogel. 

We study the effect of geometric frustration on dilational mechanical metamaterial membranes. While shape frustrated elastic plates can only accommodate nonzero Gaussian curvature up to size scales that ultimately vanish with their elastic thickness, we show that frustrated metamembranes accumulate hyperbolic curvatures up to mesoscopic length scales that are ultimately independent of the size of their microscopic constituents. A continuum elastic theory and discrete numerical model describe the size-dependent shape and internal stresses of axisymmetric, trumpetlike frustrated metamembranes, revealing a nontrivial crossover to a much weaker power-law growth in elastic strain energy with size than in frustrated elastic membranes. We study a consequence of this for the self-limiting assembly thermodynamics of frustrated trumpets, showing a severalfold increase in the size range of self-limitation of metamembranes relative to elastic membranes. 

Many complex wetting behaviors of fibrous materials are rooted in the behaviors of individual droplets attached to pairs of fibers. Here, we study the splitting of a droplet held between the tips of two cylindrical fibers. We discover a sharp transition between two post-rupture states, navigated by changing the angle between the rods, in agreement with our bifurcation analysis. Depinning of the bridge contact line can lead to a much larger asymmetry between the volume of liquid left on each rod. This second scenario enables the near-complete transfer of an aqueous glycerol droplet between two identical vinylpolysiloxane fibers. We leverage this response in a device that uses a ruck to pass a droplet along a train of fibers, a proof-of-concept for the geometric control of droplets on deformable, architected surfaces. 

While many materials exhibit a complex, hysteretic response to external driving, there has been a surge of interest in how the complex dynamics of internal materials states can be understood and designed to process and store information. We consider a system of connected rubber balloons that can be described by a Preisach model of noninteracting hysterons under pressure control but for which the hysterons become coupled under volume control. We study this system by exploring the possible transition graphs, as well as by introducing a configuration space approach which tracks the volumes of each balloon. Changes in the transition graphs turn out to be related to changes in the topology of the configuration space of the balloons, providing a particularly geometric view of how transition graphs can be designed, as well as additional information on the existence of hidden metastable states. This class of systems is more general than just balloons. 

We consider the localization of elastic waves in thin elastic structures with spatially varying curvature profiles, using a curved rod and a singly curved shell as concrete examples. Previous studies on related problems have broadly focused on the localization of flexural waves on such structures. Here, using the semiclassical WKB approximation for multicomponent waves, we show that in addition to flexural waves, extensional and shear waves also form localized, bound states around points where the absolute curvature of the structure has a minimum. We also see excellent agreement between our numerical experiments and the semiclassical results, which hinges on the vanishing of two extra phases that arise in the semiclassical quantization rule. Our findings open up novel ways to fine-tune the acoustic and vibrational properties of thin elastic structures and raise the possibility of introducing new phenomena not easily captured by effective models of flexural waves alone. 

We develop a framework to understand the mechanics of metamaterial sheets on curved surfaces. Here we have constructed a continuum elastic theory of mechanical metamaterials by introducing an auxiliary, scalar gauge-like field that absorbs the strain along the soft mode and projects out the stiff ones. We propose a general form of the elastic energy of a mechanism based metamaterial sheet and specialize to the cases of dilational metamaterials and shear metamaterials conforming to positively and negatively curved substrates in the Föppl–Von Kármán limit of small strains. We perform numerical simulations of these systems and obtain good agreement with our analytical predictions. This work provides a framework that can be easily extended to explore non-linear soft modes in metamaterial elasticity in future. 

We propose and investigate an extension of the Caspar–Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies—in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)—is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.