arXiv subjects

Christian D. Santangelo

Publications and source records attributed to Christian D. Santangelo.

At least 19 recordsLinked to original sources

arXiv2026

Twist-driven helical flattening in nematic elastomer cylinders

Liquid Crystal elastomers (LCEs) deform anisotropically along a prescribed nematic director field, making them promising candidates for programmable shape change. Existing studies have primarily focused on either director patterns on flat sheets or simple patterns on curved geometries, leaving the case of a non-trivial director on a non-trivial geometry still largely unexplored. Many biological systems, however, have both complex geometries and complex helical fiber architectures. To explore the interplay between director and underlying geometry, we use a non-Euclidean plate theory for nematic elastomers with a through-thickness twisted director to develop an effective 2D model. With a fixed twist angle, our model shows an anomalous coupling between mid-surface curvature and director twist. This emergent term arises from the interplay between orientational order and elasticity, and dominates traditional bending contributions. To illustrate the general theory, we study the stability of cylindrical shapes with through-thickness twist. We find that the cylinder is unstable to a long-wavelength helical flattening mode and determine the critical parameter for the onset of instabilities.

cond-mat.soft↗

arXiv2026

Bonded-particle model for magneto-elastic rods

We develop a bonded-particle model for magneto-elastic rods that unifies large deformations, contact, and long-range magnetic interactions within a single discrete-element framework. The rod is discretized into orientable particles connected by co-rotational bonds that capture stretching, shearing, twisting, and bending through a symmetric decomposition of relative displacement and rotation. Magnetic coupling is introduced at the particle level: each particle carries a dipole moment that rotates with it, enabling both external-field actuation and long-range dipole--dipole interactions without modifying the structural formulation. We implement the model in LAMMPS to take advantage of its parallel efficiency, long-range electrostatic solvers, and multiphysics capabilities. We validate the model on three problems spanning writhing instabilities, non-uniform magnetic actuation, and dipole-induced mechanical hysteresis. To demonstrate multiphysics capability, we couple the model with a lattice Boltzmann fluid solver via the immersed boundary method and simulate filaments in oscillatory channel flow and fluid pumping by magnetically actuated cilia arrays. Across all examples, the model shows good agreement with experimental, analytical, and numerical reference results.

cond-mat.soft↗

arXiv2026

Dynamical geometric modes in non-Euclidean plates

When subjected to specific prestresses, continuum elastic shells can exhibit geometric zero modes: complex motions that require vanishing elastic energy to excite, enabling them to be driven by weak and generic energy inputs. Despite recent interest in these modes, we understand very little about their dynamical properties. Non-Euclidean plates modeled on minimal surfaces are one example in which prestresses and geometry combine to produce a continuum of ground states that the plate can explore through a geometric zero mode. We demonstrate that a non-Euclidean plate with metric corresponding to Enneper's minimal surface exhibits the predicted continuous stability, but this degeneracy is ultimately lifted by aging. Despite developing a preferred configuration, the zero mode remains the softest mode. Using a combination of analytical theory and experiments, we show that the elastodynamics of this soft mode is captured by the dynamics of a damped pendulum. A periodic driving uncovers resonance phenomena in this pendulum mode, such as small oscillations and steady rotations, but mixes with an additional flapping mode at high frequencies.

cond-mat.soft↗

arXiv2026

Magnetoresistance and electric current oscillations induced by geometry in a two-dimensional quantum ring

In this work, we investigate the effects of a controlled conical geometry on the electric charge transport through a two-dimensional quantum ring weakly coupled to both the emitter and the collector. These mesoscopic systems are known for being able to confine highly mobile electrons in a defined region of matter. In particular, we consider a GaAs device having an average radius of $800\hspace{0.05cm}\text{nm}$ in different regimes of subband occupation at non-zero temperature and under the influence of a weak and uniform background magnetic field. Using the adapted Landauer formula for the resonant tunneling and the energy eigenvalues, we explore how the modified surface affects the Van-Hove conductance singularities, the magnetoresistance interference patterns resulting from the Aharonov-Bohm oscillations of different frequencies and the charge transport when an electric potential is applied in the terminals of the device. Magnetoresistance and charge current oscillations depending only on the curvature intensity are reported, providing a new feature that represents an alternative way to optimize the transport through the device by tuning its geometry.

cond-mat.mes-hall↗

arXiv2025

A catastrophic approach to designing interacting hysterons

We present a framework for analyzing collections of interacting hysterons through the lens of catastrophe theory. By modeling hysteron dynamics as a gradient system, we show how to construct hysteron transition graphs by characterizing the fold bifurcations of the dynamical system. Transition graphs represent the sequence of hysterons switching states, providing critical insights into the collective behavior of driven disordered media. Extending this analysis to higher codimension bifurcations, such as cusp bifurcations and crossings of fold curves, allows us to map out how the topology of transition graphs changes with variations in system parameters. This approach can suggest strategies for designing metamaterials capable of encoding targeted memory and computational functionalities, but it also highlights the rapid increase of design complexity with system size, further underscoring the computational challenges of controlling large hysteretic systems.

cond-mat.soft↗

arXiv2025

A Constrained Saddle Search Approach for Constructing Singular and Flexible Bar Frameworks

Singularity analysis is essential in robot kinematics, as singular configurations cause loss of control and kinematic indeterminacy. This paper models singularities in bar frameworks as saddle points on constrained manifolds. Given an under-constrained, non-singular bar framework, by allowing one edge to vary its length while fixing lengths of others, we define the squared length of the free edge as an energy functional and show that its local saddle points correspond to singular and flexible frameworks. Using our constrained saddle search approach, we identify previously unknown singular and flexible bar frameworks, providing new insights into singular robotics design and analysis.

cs.RO↗

arXiv2025

A Constrained Optimization Approach for Constructing Rigid Bar Frameworks with Higher-order Rigidity

We present a systematic approach for constructing bar frameworks that are rigid but not first-order rigid, using constrained optimization. We show that prestress stable (but not first-order rigid) frameworks arise as the solution to a simple optimization problem, which asks to maximize or minimize the length of one edge while keep the other edge lengths fixed. By starting with a random first-order rigid framework, we can thus design a wide variety of prestress stable frameworks, which, unlike many examples known in the literature, have no special symmetries. We then show how to incorporate a bifurcation method to design frameworks that are third-order rigid. Our results highlight connections between concepts in rigidity theory and constrained optimization, offering new insights into the construction and analysis of bar frameworks with higher-order rigidity.

math.MG↗

arXiv2025

Geometric Mechanics of Thin Periodic Surfaces

Thin surfaces are ubiquitous in nature, from leaves to cell membranes, and in technology, from paper to corrugated containers. Structural thinness imbues them with flexibility, the ability to easily bend under light loads, even as their much higher stretching stiffness can bear substantial stresses. When surfaces have periodic patterns of either smooth hills and valleys or sharp origami-like creases this can substantially modify their mechanical response. We show that for any such surface, there is a duality between the surface rotations of an isometric deformation and the in-plane stresses of a force-balanced configuration. This duality means that of the six possible combinations of global in-plane strain and out-of-plane bending, exactly three must be isometries. We show further that stressed configurations can be expressed in terms of both the applied deformation and the isometric deformation that is dual to the pattern of stress that arises. We identify constraints rooted in symplectic geometry on the three isometries that a single surface can generate. This framework sheds new light on the fundamental limits of the mechanical response of thin periodic surfaces, while also highlighting the role that continuum differential geometry plays in even sharply creased origami surfaces.

cond-mat.soft↗

arXiv2025

Topological rigidity in twisted, elastic ribbons

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.

cond-mat.soft↗

arXiv2025

Design Principles for Realizable Discrete Surface Embeddings in Physical Systems

The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary conditions, their discrete counterparts-represented as networks of vertices connected by edges-can exhibit multiple distinct embeddings for identical edge lengths. We present a systematic approach to constructing discrete meshes that yield a controlled number of embeddings. By analyzing the relationship between mesh connectivity and embedding multiplicity through rigidity theory, we develop criteria for designing meshes that minimize solution multiplicity. We demonstrate computational methods based on local matrix operations and trilateration techniques, enabling practical implementation for meshes with approximately a thousand vertices. Our analysis provides both theoretical bounds on the number of possible embeddings based on Bézout's theorem and practical guidelines for mesh construction in physical applications. Through numerical simulations, we show that this approach achieves comparable accuracy to traditional minimization methods while offering computational advantages through sequential computation. Importantly, we demonstrate that in cases where a unique smooth solution exists, local fluctuations in reconstructed shapes derived from the computational grid can serve as indicators of insufficient geometric constraints. This work bridges the gap between discrete and continuous embedding problems, providing insights for applications in 4D printing, mechanical meta-materials, and deployable structures.

cond-mat.dis-nn↗

arXiv2025

Controlling Droplets at the Tips of Fibers

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.

physics.flu-dyn↗

arXiv2025

Active Learning Design: Modeling Force Output for Axisymmetric Soft Pneumatic Actuators

Soft pneumatic actuators (SPA) made from elastomeric materials can provide large strain and large force. The behavior of locally strain-restricted hyperelastic materials under inflation has been investigated thoroughly for shape reconfiguration, but requires further investigation for trajectories involving external force. In this work we model force-pressure-height relationships for a concentrically strain-limited class of soft pneumatic actuators and demonstrate the use of this model to design SPA response for object lifting. We predict relationships under different loadings by solving energy minimization equations and verify this theory by using an automated test rig to collect rich data for n=22 Ecoflex 00-30 membranes. We collect this data using an active learning pipeline to efficiently model the design space. We show that this learned material model outperforms the theory-based model and naive curve-fitting approaches. We use our model to optimize membrane design for different lift tasks and compare this performance to other designs. These contributions represent a step towards understanding the natural response for this class of actuator and embodying intelligent lifts in a single-pressure input actuator system.

cs.RO↗

arXiv2025

Bifurcations of inflating balloons and interacting hysterons

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 non-interacting 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.

cond-mat.soft↗

arXiv2024

Geometrically frustrated, mechanical metamaterial membranes: Large-scale stress accumulation and size-selective assembly

We study the effect of geometric frustration on dilational mechanical metamaterial membranes. While shape frustrated elastic plates can only accommodate non-zero Gaussian curvature up to size scales that ultimately vanish with their elastic thickness, we show that frustrated {\it 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, trumpet-like frustrated metamembranes, revealing a non-trivial 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 several-fold increase the size range of self-limitation of metamembranes relative to elastic membranes.

cond-mat.soft↗

arXiv2024

Geometric Localization of Waves on Thin Elastic Structures

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.

cond-mat.soft↗

arXiv2023

Limits of economy and fidelity for programmable assembly of size-controlled triply-periodic polyhedra

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.

cond-mat.soft↗

arXiv2023

How cells wrap around virus-like particles using extracellular filamentous protein structures

Nanoparticles, such as viruses, can enter cells via endocytosis. During endocytosis, the cell surface wraps around the nanoparticle to effectively eat it. Prior focus has been on how nanoparticle size and shape impacts endocytosis. However, inspired by the noted presence of extracellular vimentin affecting viral and bacteria uptake, as well as the structure of coronaviruses, we construct a computational model in which both the cell-like construct and the virus-like construct contain filamentous protein structures protruding from their surfaces. We then study the impact of these additional degrees of freedom on viral wrapping. We find that cells with an optimal density of filamentous extracellular components (ECCs) are more likely to be infected as they uptake the virus faster and use relatively less cell surface area per individual virus. At the optimal density, the cell surface folds around the virus, and folds are faster and more efficient at wrapping the virus than crumple-like wrapping. We also find that cell surface bending rigidity helps generate folds, as bending rigidity enhances force transmission across the surface. However, changing other mechanical parameters, such as the stretching stiffness of filamentous ECCs or virus spikes, can drive crumple-like formation of 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 that may include filamentous ECCs.

cond-mat.soft↗

arXiv2022

Thermal Fluctuations of Singular Bar-Joint Mechanisms

A bar-joint mechanism is a deformable assembly of freely rotating joints connected by stiff bars. Here we develop a formalism to study the equilibration of common bar-joint mechanisms with a thermal bath. When the constraints in a mechanism cease to be linearly independent, singularities can appear in its shape space, which is the part of its configuration space after discarding rigid motions. We show that the free-energy landscape of a mechanism at low temperatures is dominated by the neighborhoods of points that correspond to these singularities. We consider two example mechanisms with shape-space singularities and find that they are more likely to be found in configurations near the singularities than others. These findings are expected to help improve the design of nanomechanisms for various applications.

cond-mat.soft↗