arXiv subjects

Tomohiko G. Sano

Publications and source records attributed to Tomohiko G. Sano.

At least 19 recordsLinked to original sources

arXiv2026

Numerical and experimental framework for bending elasticity of highly flexible slender structures

Slender structures are highly flexible, spanning several orders of magnitude in length scale. Their deformation depends on the slenderness of their cross sections, highlighting that the elasticity and geometry of structures are intrinsically coupled. The deformation of the cross-section becomes significant, particularly when tubes and pipes are subjected to bending, known as the Brazier instability. Although the bending performance of slender structures is quantified experimentally using a canonical three-point bending test, their numerical counterparts remain under-explored because complex contact mechanics must be implemented in simulations. In this study, we develop a computational framework to simulate experimental three-point bending tests using a hybrid material point method (hybrid-MPM) approach, which integrates Lagrangian finite element and Eulerian finite difference frameworks. We adapt our framework to elastic tubes and tape springs as canonical examples that exhibit characteristic bending deformation in which the cross-sectional and lengthwise bending are coupled. The predictions of numerical simulations are validated against desktop experiments and classical theory. The excellent agreement between the simulation and the experiments implies that the hybrid-MPM framework provides a robust computational framework for predicting the large deformation of structures involving complex contact, such as soft robots and deployable structures.

cond-mat.soft↗

arXiv2026

Where Humpty Dumpty Breaks: Geometry-Driven Fracture in Ellipsoidal Shells

Fracture networks are ubiquitous in nature, spanning scales from millimeter-sized cracks in botanical peels to hundred-kilometer-long lineae on planetary satellites. The propagation of a crack is a complex, nonlinear phenomenon governed by the interplay of mechanical properties, rheological behavior, and system geometry. While fracture mechanics has long addressed structural failure, the relationship among fracture, elasticity, and nonlinear geometry has recently revived as a focal point in condensed matter and biophysics. However, a unified framework that systematically explains how surface geometry prescribes the transition between disparate fracture morphologies remains elusive. Here we show that shell curvature provides a geometric blueprint for fracture, governing the evolution of complex crack networks through induced stress anisotropy. By internally pressurizing thin, bilayer spheroidal shells, we demonstrate that a rich diversity of crack morphologies across lateral, longitudinal, and random orientations depends on the curvature ratio between the pole and the equator. We find that these patterns arise from the nonlinear mechanics of the shell, which can be leveraged to effectively control crack growth. Our results establish a direct link between structural curvature and fractures, providing a predictive framework that integrates nonlinear geometry with the classical Griffith and von Mises criteria. Beyond our model system, we find that the disparate fracture patterns observed in ripening muskmelons and in the icy crust of Europa follow the same geometric principles. We expect that this unified understanding of crack morphogenesis will inform the design principles of novel functional materials that are resilient to fracture and provide insights into the mechanical performance of curved biological and geophysical architectures.

cond-mat.soft↗

arXiv2025

Buckling of knitted fabric wrapped around a rigid cylinder

Knitted fabrics exhibit high flexibility due to their periodic loop structures formed by bent yarns. Under compressive loading, they develop three-dimensional (3D) wrinkling patterns that reflect nonlinear interactions between yarn elasticity and local loop deformations, as observed when the sleeves of a sweater are rolled up. Despite their widespread use in garments and medical textiles, the relationship between loop-level geometry and macroscopic buckling remains less understood. Here, we investigate the 3D deformation of knitted fabrics wrapped around a rigid cylinder under uniaxial compression. Circumferential and axial stitch numbers are systematically varied to determine how loop geometry affects the evolution of wrinkle patterns. Samples with a small number of circumferential stitches exhibit sequential wrinkle formation from the compressed end, leading to an accordion-like wrinkle pattern, whereas those with a larger number of stitches form helical wrinkles simultaneously across the surface. Wrinkle morphology changes progressively with stitch geometry, accompanied by systematic variations in compressive force, loop deformation, and helical wrinkle angle. The development of helical wrinkles originates from subtle structural asymmetries introduced during manufacturing processes, including the tension applied during knitting and the direction of sample assembly. These results demonstrate that small variations in local loop deformation can lead to substantial differences in wrinkle morphology, highlighting the sensitivity of macroscopic buckling to microscopic structural features. The study establishes a direct link between loop-level mechanics and global deformation behavior, providing a basis for the predictive design of knitted structures with tailored mechanical responses and complex 3D patterns.

cond-mat.soft↗

arXiv2025

Sliding of cylindrical shell into a rigid hole

Fitting two different materials is a versatile methodology in manufacturing complex structures. One of the canonical models for fitting is the snap-fit model, in which flexible materials and rigid structures are assembled by pushing their interlocking components together. The assembly via snap-fit is often accompanied by large deformations of flexible structures and abrupt force drops, highlighting the role of elasticity, geometry, and contact friction. Despite several model studies revealing fundamental mechanics for snap-fit, the current snap-fit design relies on prototyping and empirical rules. In this paper, we analyze a snap-fit model in which a naturally curved beam slips into a rigid hole. We construct an analytical model based on the theory of elastica with contact friction and demonstrate that its predictions are in excellent quantitative agreement with both simulations and experiments. We find three distinct sliding modes: Folding, Pinning, and Unfolding. The classification is systematically organized in a phase diagram based on the geometric parameters of the shells and the hole. Our study complements existing approaches by providing a predictive framework for contact-based structures that involve friction, elasticity, and geometry, and sheds light on a unified understanding of the interactions between an elastic and a rigid body.

cond-mat.soft↗

arXiv2025

(Dis)continuous buckling transition in elastic shell mediated by contact

Snap-buckling is a rapid shape transition in slender structures, appearing as a fundamental switching mechanism of natural and man-made systems. Boundary conditions of structures are crucial to predict and control their snap-buckling behavior. However, the general framework that relates boundary conditions, geometry, and performance of structures is still absent to date. Here, we study the snap-buckling of hemispherical shells in contact with rigid cylinders of different diameters to uncover the roles of boundary conditions in the dynamic performance of shells. Specifically, we analyze the jumping dynamics of the pneumatically inverted shells placed on the rigid cylinder by combining experiments and analytical theory. We find the characteristic diameter classifying the snap-buckling and jumping dynamics into two: (i)~if the diameter of the cylinder is sufficiently larger than the characteristic diameter, the shell is regarded as in contact with the infinitely large flat plate, (ii)~if not, the cylinder is regarded as a point. The analytical predictions for the jumping performance of the shell supplemented with the characteristic diameter are in excellent agreement with our experimental results. Our study clarifies that contact geometry is crucial in predicting the pathway of snap-buckling, indicating that the dynamic performance of soft robots would be optimized by tuning their surface geometry.

cond-mat.soft↗

arXiv2025

Twist deformation of physical trefoil knots

Knots across various length scales, from micro to macro-scales, such as polymers, DNA, shoelaces, and surgery, serving their unique mechanical properties. The shape of ideal knots has been extensively studied in the context of knot theory, while that of physical knots has been discussed very recently. The complex interplay of elasticity and geometry, such as bending, twisting, and contact, needs to be disentangled to predict their deformation. Still, the unified understanding of the deformation of physical knots is insufficient. Here, we focus on the trefoil knot, a closed knot with a nontrivial topology, and study the relationship between the shapes of the trefoil knot and applied physical twists, combining experiments and simulations. As we twist the elastomeric rod, the knot becomes either tightened or loosened, preserving the original three-fold symmetry, and then buckles and exhibits symmetry breaking at critical angles. The curvature profiles computed through the X-ray tomography analysis also exhibit similar symmetry breaking. The transition would be triggered by the mechanical instability, where the imposed twist energy is converted into the bending energy. The phase transition observed here is analogous to the classical buckling phenomena of elastic rings known as the Michell instability. We find that the twist buckling instability of the trefoil knot results from the interplay of bending, twisting, and contact properties of the rod. In other words, the buckling of the knot is predictable based on the elasticity and geometry of rods, which would be useful in avoiding or even utilizing their buckling in practical engineering applications such as surgery and the shipping industry.

cond-mat.soft↗

arXiv2024

Snap and Jump: How Elastic Shells Pop Out

Grip, walk, crawl, and jump. Soft robots are integrated functional structures composed of compliant mechanisms, whose activity spans various industrial applications such as surgery, healthcare, surveillance, and even planetary exploration. One of their promising mobility mechanism is snap-buckling; the instability mode of flexible structures passing from one equilibrium state to another can instantaneously generate large power for its motion. Predicting their performance with even simple geometry requires disentangling material, geometric nonlinearity, and contact, thereby still being a challenging problem to date. Here, we study the jumping dynamics of hemispherical elastic shells driven by snap-buckling, as a model system of soft jumping mechanisms, combining experiments, simulations, and analytical theory. We find that the contact transition dynamics trigger the jumping phenomenon upon snap-buckling by constructing the analytical predictions with shell elasticity in excellent agreement with both experiments and simulations. Despite the simple geometry of the shell, its dynamical performance primarily relies on a complex interplay between elasticity, geometry, and contact friction. By elucidating the dynamics of the building blocks of soft robots that undergo large deformations, we can build their predictive experimental and numerical framework. Our research paves the way for designing soft robots suitable for the required loading conditions or structural requirements without empirical methods.

cond-mat.soft↗

arXiv2024

Curling morphology of knitted fabrics: Structure and Mechanics

Knitted fabrics are two-dimensional-like structures formed by stitching one-dimensional yarn into three-dimensional curves. Plain stitch or stockinette stitch, one of the most fundamental knitting stitches, consists of periodic lattices of bent yarns, where three-dimensional (3D) curling behavior naturally emerges at the edges. The elasticity and geometry of knitted fabrics have been studied in previous studies, primarily based on 2D modeling. Still, the relation between 3D geometry and the mechanics of knitted fabrics has not been clarified so far. The curling behavior of knits is intricately related to the forces and moments acting on the yarns, geometry of the unit knitted loops, mechanical properties, and contacts, hence requiring a 3D analysis. Here, we show that the curling of plain knits emerges through the elasticity and geometry of the knitted loops, combining desktop-scale experiments and reduced elasticity-based simulations. We find that by changing the horizontal and vertical knitting numbers, three types of curl shapes emerge: side curl and top/bottom curl shapes, which are curled only horizontally and vertically, and double curl shape, in which both curl shapes appear together. The fundamental mechanism of intricate shape deformation is clarified through the force and moment balance along yarn whose centerline shape is discretized through the B-spline curves where elastic stretching, bending, and contact mechanics are taken into account. We reveal that the 3D structure of the single-knitted loop plays a critical role in the curling behavior. Our results imply that the change in shape per a single knitted loop has the potential to control the 3D natural overall shape of knitted fabrics, and could be applied in predicting or designing more complex 3D shapes made of knitted fabrics.

cond-mat.soft↗

arXiv2023

Randomly stacked open-cylindrical shells as a functional mechanical device

Structures with artificial mechanical properties, often called mechanical metamaterials, exhibit divergent yet tunable performance. Various types of mechanical metamaterials have been proposed, which harness light or magnetic interactions, structural instabilities in slender or hollow structures, and contact friction. However, most of the designs are precisely engineered without any imperfections, in order to perform as programmed. Here, we study the mechanical performance of randomly stacked cylindrical-shells, which act as a disordered mechanical metamaterial. Combining experiments and simulations, we demonstrate that the stacked shells can absorb and store mechanical energy upon compression by exploiting large deformation and relocation of shells, snap-fits, and friction. Although shells are oriented randomly, the system exhibits robust mechanical performance controlled by friction and geometry. Our results demonstrate that the rearrangement of flexible components could yield versatile but predictive mechanical responses.

cond-mat.soft↗

arXiv2022

Snap buckling of bistable beams under combined mechanical and magnetic loading

We investigate the mechanics of bistable, hard-magnetic, elastic beams, combining experiments, finite element modeling (FEM), and a reduced-order theory. The beam is made of a hard magneto-rheological elastomer, comprising two segments with antiparallel magnetization along the centerline, and is set into a bistable curved configuration by imposing an end-to-end shortening. Reversible snapping is possible between these two stable states. First, we experimentally characterize the critical field strength for the onset of snapping, at different levels of end-to-end shortening. Second, we perform 3D FEM simulations using the Riks method to analyze high-order deformation modes during snapping. Third, we develop a reduced-order centerline-based beam theory to rationalize the observed magneto-elastic response. The theory and simulations are validated against experiments, with an excellent quantitative agreement. Finally, we consider the case of combined magnetic and mechanical-indentation loading, examining how the applied field affects the bistability and quantifying the maximum load-bearing capacity. Our work provides a set of predictive tools for the rational design of one-dimensional, bistable, magneto-elastic structural elements.

cond-mat.soft↗

arXiv2021

A Kirchhoff-like theory for hard magnetic rods under geometrically nonlinear deformation in three dimensions

Magneto-rheological elastomers (MREs) are functional materials that can be actuated by applying an external magnetic field. MREs comprise a composite of hard magnetic particles dispersed into a nonmagnetic elastomeric matrix. By applying a strong magnetic field, one can magnetize the structure to program its deformation under the subsequent application of an external field. Hard MREs, whose coercivities are large, have been receiving particular attention because the programmed magnetization remains unchanged upon actuation. Hence, once a structure made of a hard MRE is magnetized, it can be regarded as magnetized permanently. Motivated by a new realm of applications, there have been significant theoretical developments in the continuum description of hard MREs. By reducing the 3D description into 1D or 2D via dimensional reduction, several theories of hard magnetic slender structures such as linear beams, elastica, and shells have been recently proposed. In this paper, we derive an effective theory for MRE rods under geometrically nonlinear 3D deformation. Our theory is based on reducing the 3D magneto-elastic energy functional for the hard MREs into a 1D Kirchhoff-like description. Restricting the theory to 2D, we reproduce previous works on planar deformations. For further validation in the general case of 3D deformation, we perform precision experiments with both naturally straight and curved rods under either constant or constant-gradient magnetic fields. Our theoretical predictions are in excellent agreement with both discrete simulations and precision-model experiments. Finally, we discuss some limitations of our framework, as highlighted by the experiments, where long-range dipole interactions, which are neglected in the theory, can play a role.

cond-mat.soft↗

arXiv2021

The shapes of physical trefoil knots

We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed and open configurations. Ideal knots are purely geometric abstractions for the tightest configuration tied in a perfectly flexible, self-avoiding tube with an inextensible centerline and undeformable cross-sections. Here, we construct physical realizations of tight trefoil knots tied in an elastomeric rod, and use X-ray tomography and 3D finite element simulation for detailed characterization. Specifically, we evaluate the role of elasticity in dictating the physical knot's overall shape, self-contact regions, curvature profile, and cross-section deformation. We compare the shape of our elastic knots to prior computations of the corresponding ideal configurations. Our results on tight physical knots exhibit many similarities to their purely geometric counterparts, but also some striking dissimilarities that we examine in detail. These observations raise the hypothesis that regions of localized elastic deformation, not captured by the geometric models, could act as precursors for the weak spots that compromise the strength of knotted filaments.

cond-mat.soft↗

arXiv2020

Technical Brief: Finite Element Modeling of Tight Elastic Knots

We present a methodology to simulate the mechanics of knots in elastic rods using geometrically nonlinear, full three-dimensional (3D) finite element analysis. We focus on the mechanical behavior of knots in tight configurations, for which the full 3D deformation must be taken into account. To set up the topology of our knotted structures, we apply a sequence of prescribed displacement steps to the centerline of an initially straight rod that is meshed with 3D solid elements. Self-contact is enforced with a normal penalty force combined with Coulomb friction. As test cases, we investigate both overhand and figure-of-eight knots. Our simulations are validated with precision model experiments, combining rod fabrication and X-ray tomography. Even if the focus is given to the methods, our results reveal that 3D deformation of tight elastic knots is central to their mechanical response. These findings contrast to a previous analysis of loose knots, for which 1D centerline-based rod theories sufficed for a predictive understanding. Our method serves as a robust framework to access complex mechanical behavior of tightly knotted structures that are not readily available through experiments nor existing reduced-order theories.

cond-mat.soft↗

arXiv2020

Mechanics of two filaments in tight contact: The orthogonal clasp

Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear deformations, and friction. Here, we perform an in-depth study of a simple yet canonical problem that captures the essence of contact between filaments. In the orthogonal clasp, two filaments are brought into contact, with each centerline lying in one of a pair of orthogonal planes. Our data from X-ray tomography (micro-CT) and mechanical testing experiments are in excellent agreement with the finite element method (FEM) simulations. Despite the apparent simplicity of the physical system, the data exhibits strikingly unintuitive behavior, even when the contact is frictionless. Specifically, we observe a curvilinear diamond-shaped ridge in the contact pressure field between the two filaments, sometimes with an inner gap. When a relative displacement is imposed between the filaments, friction is activated, and a highly asymmetric pressure field develops. These findings contrast to the classic capstan analysis of a single filament wrapped around a rigid body. Both the micro-CT and the FEM data indicate that the cross-sections of the filaments can deform significantly. Nonetheless, an idealized geometrical theory assuming undeformable tube cross-sections and neglecting elasticity rationalizes our observations qualitatively and highlights the central role of the small but finite tube radius of the filaments. We believe that our orthogonal clasp analysis provides a building block for future modeling efforts in frictional contact mechanics of more complex filamentary structures.

cond-mat.soft↗

arXiv2019

Loopy Lévy flights enhance tracer diffusion in active suspensions

Brownian motion is widely used as a paradigmatic model of diffusion in equilibrium media throughout the physical, chemical, and biological sciences. However, many real world systems, particularly biological ones, are intrinsically out-of-equilibrium due to the energy-dissipating active processes underlying their mechanical and dynamical features. The diffusion process followed by a passive tracer in prototypical active media such as suspensions of active colloids or swimming microorganisms indeed differs significantly from Brownian motion, manifest in a greatly enhanced diffusion coefficient, non-Gaussian tails of the displacement statistics, and crossover phenomena from non-Gaussian to Gaussian scaling. While such characteristic features have been extensively observed in experiments, there is so far no comprehensive theory explaining how they emerge from the microscopic active dynamics. Here we present a theoretical framework of the enhanced tracer diffusion in an active medium from its microscopic dynamics by coarse-graining the hydrodynamic interactions between the tracer and the active particles as a stochastic process. The tracer is shown to follow a non-Markovian coloured Poisson process that accounts quantitatively for all empirical observations. The theory predicts in particular a long-lived Lévy flight regime of the tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, thus suggesting that the optimal foraging strategy of swimming microorganisms might crucially depend on the density in order to exploit the Lévy flights of nutrients. Our framework provides the first validation of the celebrated Lévy flight model from a physical microscopic dynamics.

cond-mat.stat-mech↗

arXiv2018

Twist-induced snapping in a bent elastic ribbon

Snapping of a slender structure is utilized in a wide range of natural and man-made systems, mostly to achieve rapid movement without relying on muscle-like elements. Although several mechanisms for elastic energy storage and rapid release have been studied in detail, a general understanding of the approach to design such a kinetic system is a key challenge in mechanics. Here we study a twist-driven buckling and fast flip dynamics of a geometrically constraint ribbon by combining experiments, numerical simulations, and analytical theory. We identify two distinct types of shape transitions; a narrow ribbon snaps, whereas a wide ribbon forms a pair of localized helices. We construct a phase diagram and explain the origin of the boundary, which is determined only by geometry. We quantify effects of gravity and clarify time scale dictating the rapid flipping. Our study reveals the unique role of geometric twist-bend coupling on the fast dynamics of a thin constrained structure, which has implications for a wide range of biophysical and applied physical problems.

cond-mat.soft↗

arXiv2017

Anomalous snapping behavior in asymmetrically constrained elastic strips

When a flat elastic strip is compressed along its axis, it is bent in one of two possible directions via spontaneous symmetry breaking and forms a cylindrical arc, a phenomenon well known as Euler buckling. When this cylindrical section is pushed in the other direction, the bending direction can suddenly reverse. This instability is called snap-through buckling and is one of the elementary shape transitions in a prestressed thin structure. Combining experiments and theory, we study snap-buckling of an elastic strip with one end hinged and the other end clamped. These asymmetric boundary constraints break the intrinsic symmetry of the strip, generating rich exotic mechanical behaviors including largely hysteretic but reproducible force responses and switch-like discontinuous shape changes. We establish the set of exact analytical solutions that fully explain all of our major experimental and numerical findings. Asymmetric boundary conditions arise naturally in diverse situations when a thin object is in contact with a solid surface at one end, but their profound consequences for the buckling mechanics have been largely overlooked to date. The idea of introducing asymmetry through boundary conditions would yield new insight into complex and programmable functionalities in material and industrial design.

cond-mat.soft↗

arXiv2017

Slip Morphology of Elastic Strips on Frictional Rigid Substrates

The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate is investigated by a combination of theory and experiment. We find a rich variety of morphologies, which -when the bending elasticity dominates over the effect of gravity- are classified into three distinct types of states: pinned, partially slipped, and completely slipped, depending on the magnitude of the vertical strain and coefficient of static friction. We develop a theory of elastica under mixed clamped-hinged boundary conditions combined with the Coulomb-Amontons friction law, and find excellent quantitative agreement with simulations and controlled physical experiments. We also discuss the effect of gravity in order to bridge the difference in qualitative behaviors of stiff strips and flexible strings, or ropes. Our study thus complements recent work on elastic rope coiling, and takes a significant step towards establishing a unified understanding of how a thin elastic object interacts vertically with a solid surface.

cond-mat.soft↗