Elastic Backbone Research Articles

Rapid 3D printing of electro-active hydrogels

Electroactive hydrogels (EAH) have gained prominence for their unique ability to change shape or size under an electric field, finding applications in biosensors and soft actuators. This study focuses on a tunnelable EAH tailored for high-resolution 3D printing via the micro continuous liquid interface production (µCLIP) process. The resin formulations mainly involve acrylic acid (AA) and 4-hydroxybutyl acrylate (4-HBA). AA, with its carboxyl groups, introduces electroactuation, generating osmotic pressure in the hydrogel matrix. This results in swelling, inducing bending towards the cathode, accentuating the material’s responsiveness. In contrast, 4-HBA offers mechanical resilience, providing an elastic backbone, and ensuring the hydrogel’s applicability. Our results illustrate the hydrogel’s strength, flexibility, and bending capabilities across varied compositions and electric field strengths. Notably, the µCLIP process enabled the 3D printing of our EAH into sophisticated structures, like the lattice. The combination of AA’s electro-responsive traits with 4-HBA’s durability has birthed a material with vast practical implications. This study provides extended potential breakthroughs in soft robotics, wearable electronics, and medical devices, marking a significant stride in the realm of electroactive materials.

An anisotropic damage visco-hyperelastic model for multiaxial stress-strain response and energy dissipation in filled rubber

In this article, we introduce a novel physically-based anisotropic damage visco-hyperelastic model designed to predict the history-dependent inelastic behavior of multiaxially stretched filled rubber. The model integrates both the anisotropic Mullins effect and intrinsic viscosity through the consideration of internal physics, represented by two distinct networks: an elastic ground network and a superimposed viscous network. The rupture of molecular bonds within the elastic network chain backbone is modeled using statistical mechanics, while the effects of anisotropy-induced chain orientation at the upper scale are addressed through a microsphere-based scale transition method. The intrinsic viscosity is represented by the viscous network, which is governed by time-dependent equations to account for the viscous overstress. The influence of fillers is captured through the concept of strain amplification, applied to the two networks within the rubber matrix. The effectiveness of the model in capturing the biaxial behavior of filled rubber is evaluated by comparing its outputs with experimental data from a filled rubber system. This assessment specifically considers the impact of pre-stretching under various loading conditions and across a wide range of filler concentrations. Notably, it successfully predicts anisotropic stress-strain response and energy dissipation, and the coupled effects of damage and viscosity.

Cross-streamline migration and near-wall depletion of elastic fibers in micro-channel flows.

The complex dynamics of elastic fibers in viscous fluids are central to many biological and industrial systems. Fluid-structure interactions underlying these dynamics govern the shape and transport of flexible fibers, and understanding these interactions can help tune flow properties in applications such as microfluidic separation, printing and clogging. In this work, we use slender-body theory to study micromechanical dynamics that arise from the coupling between the elastic backbone of a fiber and the local straining flow that contributes to filament flipping and cross-streamline migration. The resulting transverse drift is unbiased in either direction in simple shear flow. However, a non-uniform shear rate results in bias towards regions of high shear, which we connect to the shape transitions during flips. We discover a depletion layer that forms near the boundaries of pressure-driven channel flow due to the competition between such a cross-streamline drift and steric exclusion from the walls. Finally, we develop scaling laws for the curvature of filaments during flip events, demonstrating the origin of the drift bias in non-uniform flows, and confirm this behavior from our simulations. Put together, these results shed light on the role of a local and dominant coupling between elasticity and viscous resistance in dictating long-term dynamics and transport of elastic fibers in confined flows.

Multi-characteristic tannic acid-reinforced polyacrylamide/sodium carboxymethyl cellulose ionic hydrogel strain sensor for human-machine interaction

Big data and cloud computing are propelling research in human-computer interface within academia. However, the potential of wearable human-machine interaction (HMI) devices utilizing multiperformance ionic hydrogels remains largely unexplored. Here, we present a motion recognition-based HMI system that enhances movement training. We engineered dual-network PAM/CMC/TA (PCT) hydrogels by reinforcing polyacrylamide (PAM) and sodium carboxymethyl cellulose (CMC) polymers with tannic acid (TA). These hydrogels possess exceptional transparency, adhesion, and remodelling features. By combining an elastic PAM backbone with tunable amounts of CMC and TA, the PCT hydrogels achieve optimal electromechanical performance. As strain sensors, they demonstrate higher sensitivity (GF = 4.03), low detection limit (0.5 %), and good linearity (0.997). Furthermore, we developed a highly accurate (97.85 %) motion recognition system using machine learning and hydrogel-based wearable sensors. This system enables contactless real-time training monitoring and wireless control of trolley operations. Our research underscores the effectiveness of PCT hydrogels for real-time HMI, thus advancing next-generation HMI systems.

Lightweight Pneumatically Elastic Backbone Structure with Modular Construction and Nonlinear Interaction for Soft Actuators.

There has been a growing need for soft robots operating various force-sensitive tasks due to their environmental adaptability, satisfactory controllability, and nonlinear mobility unique from rigid robots. It is of desire to further study the system instability and strongly nonlinear interaction phenomenon that are the main influence factors to the actuations of lightweight soft actuators. In this study, we present a design principle on lightweight pneumatically elastic backbone structure (PEBS) with the modular construction for soft actuators, which contains a backbone printed as one piece and a common strip balloon. We build a prototype of a lightweight (<80 g) soft actuator, which can perform bending motions with satisfactory output forces (∼20 times self-weight). Experiments are conducted on the bending effects generated by interactions between the hyperelastic inner balloon and the elastic backbone. We investigated the nonlinear interaction and system instability experimentally, numerically, and parametrically. To overcome them, we further derived a theoretical nonlinear model and a numerical model. Satisfactory agreements are obtained between the numerical, theoretical, and experimental results. The accuracy of the numerical model is fully validated. Parametric studies are conducted on the backbone geometry and stiffness, balloon stiffness, thickness, and diameter. The accurate controllability, operation safety, modularization ability, and collaborative ability of the PEBS are validated by designing PEBS into a soft laryngoscope, a modularized PEBS library for a robotic arm, and a PEBS system that can operate remote surgery. The reported work provides a further applicability potential of soft robotics studies.

A Mechanical Picture of Fractal Darcy’s Law

The main goal of this manuscript is to generalize Darcy’s law from conventional calculus to fractal calculus in order to quantify the fluid flow in subterranean heterogeneous reservoirs. For this purpose, the inherent features of fractal sets are scrutinized. A set of fractal dimensions is incorporated to describe the geometry, morphology, and fractal topology of the domain under study. These characteristics are known through their Hausdorff, chemical, shortest path, and elastic backbone dimensions. Afterward, fractal continuum Darcy’s law is suggested based on the mapping of the fractal reservoir domain given in Cartesian coordinates xi into the corresponding fractal continuum domain expressed in fractal coordinates ξi by applying the relationship ξi=ϵ0(xi/ϵ0)αi−1, which possesses local fractional differential operators used in the fractal continuum calculus framework. This generalized version of Darcy’s law describes the relationship between the hydraulic gradient and flow velocity in fractal porous media at any scale including their geometry and fractal topology using the αi-parameter as the Hausdorff dimension in the fractal directions ξi, so the model captures the fractal heterogeneity and anisotropy. The equation can easily collapse to the classical Darcy’s law once we select the value of 1 for the alpha parameter. Several flow velocities are plotted to show the nonlinearity of the flow when the generalized Darcy’s law is used. These results are compared with the experimental data documented in the literature that show a good agreement in both high-velocity and low-velocity fractal Darcian flow with values of alpha equal to 0&lt;α1&lt;1 and 1&lt;α1&lt;2, respectively, whereas α1=1 represents the standard Darcy’s law. In that way, the alpha parameter describes the expected flow behavior which depends on two fractal dimensions: the Hausdorff dimension of a porous matrix and the fractal dimension of a cross-section area given by the intersection between the fractal matrix and a two-dimensional Cartesian plane. Also, some physical implications are discussed.

Quantifying Bypass Traffic in Partially Meshed Transparent Optical Networks

This work investigates the transparent bypassing capacity requirements of elastic backbone optical networks to determine the all-optical cross-connection capacity needed at network nodes. Topological parameters have been used to develop a random network generator, and the generated topologies are evaluated. Reference values are obtained and applied to well-known topologies, and extensive simulations are conducted to obtain network nodes' bypassing traffic under realistic traffic profiles. The study reveals that although bypassing traffic varies by topology, it never exceeds 9% of total network traffic per node degree. These findings can help properly dimension network nodes by determining the necessary quantity of transceivers and cross-connection capacity based on the network topology and expected traffic.

Micro-mechanical insights into the stress transmission in strongly aggregating colloidal gel.

Predicting the mechanical response of soft gel materials under external deformation is of paramount importance in many areas, such as foods, pharmaceuticals, solid-liquid separations, cosmetics, aerogels, and drug delivery. Most of the understanding of the elasticity of gel materials is based on the concept of fractal scaling with very few microscopic insights. Previous experimental observations strongly suggest that the gel material loses the fractal correlations upon deformation and the range of packing fraction up to which the fractal scaling can be applied is very limited. In addition, correctly implementing the fractal modeling requires identifying the elastic backbone, which is a formidable task. So far, there is no clear understanding of the gel's elasticity at high packing fractions or the correct length scale that governs its mechanical response. In this work, we undertake extensive numerical simulations to elucidate the different aspects of stress transmission in gel materials. We observe the existence of two percolating networks of compressive and tensile normal forces close to the gel point. We also find that the probability distribution for the compressive and tensile parts normalized by their respective mean shows a universal behavior irrespective of various values of interaction potential and thermal energy and different particle size distributions. Interestingly, there are also a large number of contacts with zero normal force, and, consequently, a peak in the normal force distribution is observed at fn ≈ 0 even at higher pressures. We also identify the critical internal state parameters, such as the mean normal force, force anisotropies, and the average coordination number, and propose simple constitutive relations that relate different components of stress to internal state parameters. The agreement between our model prediction and the simulation observation is excellent. It is shown that the anisotropy in the force networks gives rise to the normal stress difference in soft gel materials. Our results strongly demonstrate that the mechanical response of the gel system is governed mainly by the particle length scale phenomena, with a complex interplay between the compressive and tensile forces at the particle contact.

SpringWorm: A Soft Crawling Robot with a Large-Range Omnidirectional Deformable Rectangular Spring for Control Rod Drive Mechanism Inspection.

In this article, a cable-driven elastic backbone worm-like robot (named "SpringWorm") of decimeter-level size is designed, which has high adaptability in crack inspection of the weld between reactor pressure vessel (RPV) and control rod drive mechanisms. The robot consists of a body that adopts a rectangular helix spring backbone driven by four cables and the flexible claws embedded with distributed electromagnets. Combining the omnidirectional deformation of the backbone and the passive deformation adsorption of the claws, the robot can achieve a variety of gaits. Based on the approaches of geometric analysis and transformation matrices of the coordinate frame, a kinematic model of the cable-driven backbone has been established. Moreover, a mechanical model considering the friction between the cable and the backbone has also been established. The top position and the bending angle of the backbone obtained by the theory, simulation, and experiment are in good agreement. In addition, the errors of the driving force between simulation and experimental results are also small. SpringWorm is 670 g, measures 206 × 65 × 75 mm, has a maximum speed of 8.9 mm/s, and has a maximum payload of 1 kg. The robot can climb over 2-cm-tall steps and 4-cm-deep ditches, and climb and turn on the vertical wall, on the pipe with a radius of 31 cm, and on the spherical surface of RPV.

The elastic and directed percolation backbone

We argue that the elastic backbone (EB) (union of shortest paths) on a cylindrical system, studied by Sampaio Filho et al [2018 Phys. Rev. Lett. 120 175701], is in fact the backbone of two-dimensional directed percolation (DP). We simulate the EB on the same system as considered by these authors, and also study the DP backbone directly using an algorithm that allows backbones to be generated in a completely periodic manner. We find that both the EB in the bulk and the DP backbone have a fractal dimension of d b = d B,DP = 1.681 02(15) at the identical critical point p c,DP ≈ 0.705 485 22. We also measure the fractal dimension at the edge of the EB system and for the full DP clusters, and find d e = d DP = 1.840 54(4). We argue that those two fractal dimensions follow from the DP exponents as d B,DP = 2 − 2β/ν ∥ = 1.681 072(12) and d DP = 2 − β/ν ∥ = 1.840 536(6). Our fractal dimensions differ from the value 1.750(3) found by Sampaio Filho et al.

Eccentric Tube Robots as Multiarmed Steerable Sheaths.

This paper presents a novel continuum robot sheath for use in single-port minimally invasive procedures such as neuroendoscopy in which the sheath is designed to deliver multiple robotic arms. Actuation of the sheath is achieved by using precurved superelastic tubes lining the working channels used for arm delivery. These tubes perform a similar role to push/pull tendons, but can accomplish shape change of the sheath via rotation. A kinematic model using Cosserat rod theory is derived which is based on modeling the system as a set of eccentrically aligned precurved tubes constrained along their length by an elastic backbone. The specific case of a two-arm sheath is considered in detail. Simulation and experiments are used to investigate the validate the concept and model.

RBM20 ASOs improve ventricular filling in a mouse model with increased titin-based stiffness

The giant protein titin provides the elastic backbone of the myofilament and is extensively spliced to adapt the mechanical properties of the ventricle. The titin splice factor RBM20 determines not only the elastic but also the contractile properties of the cardiac ventricle. Animal models that replicate phenotypic features of heart failure with preserved ejection fraction (HFpEF), such as increased stiffness of the cardiac ventricle, respond to a 50% reduction in RBM20 levels with improved diastolic filling and improved cardiac function.

Design and analysis of hybrid-driven origami continuum robots with extensible and stiffness-tunable sections

Tendon-driven continuum robots have increasingly attracted attention these years. Conventionally, such kind of robots utilizes elastic central backbones to hold the structure, which makes the robots inextensible, as well as reduces the dexterity and the workspace. Inspired by the reconfigurable feature of origami structures, this paper presents the design, analysis, and validation of a hybrid-driven continuum robot without an elastic backbone. The fabric-based, soft, and unstretchable origami pneumatic chamber holds the continuum structure and makes the robot exhibit a high extension ratio, low input pressure, and no radial expansion. With the antagonistic actuation of tendon-pulling and air-pushing, the robot can perform 3DoF motion with variable stiffness. The kinetostatics modeling and analysis are developed based on a discretization-based approach to predict the motion behavior and control the proposed robot. To validate the proposed design principle and the modeling method, a prototype is built, on which a series of experiments have been conducted. The results show that, with the proposed kinetostatics model, the prototype possesses acceptable positioning accuracy and tracking performances, while the structural stiffness can also be effectively adjusted.

A comparative performance-based seismic assessment of strongback steel braced frames

A recently introduced structural steel braced frame known as the strongback system (SBS) is a hybrid of a conventional bracing system and an essentially elastic vertical truss. This elastic backbone is designed to distribute seismic demands uniformly over the height of the building and consequently prevent damage concentration. Recent studies on developing design procedures for SBSs revealed that prescriptive code-based methods are inadequate to estimate their seismic demands, and they cannot ensure to fulfill the performance objectives properly. Here, to properly evaluate the seismic behavior of a wide variety of the practical configurations of SBS, a comprehensive parametric study is carried out on elastic backbone configuration, rigidity, and height. To this end, a series of different SBS archetypes are designed using a direct performance-based method, and the fulfillment of the performance targets is probabilistically assessed. Their over-strength factors, ductility ratios, and collapse fragility curves are compared together and with the performance of structures using conventional system and design method. Results indicate that the archetypes with the brace intersection point of two-third of the length of the beam, namely X-2/3 configuration, have shown the largest ductility ratio and lowest collapse probability, while the archetypes with chevron configuration have shown the smallest ductility ratio and highest collapse probability. Further, by increasing the rigidity of the vertical backbone, ductility ratio and the median spectral acceleration at collapse level are improved, and SBS archetypes tended to have uniform story drift distribution patterns. Applying the direct performance-based method in six-story structures reduces the story drift ratios of SBS up to 30%.

Magnetic handshake materials as a scale-invariant platform for programmed self-assembly

Programmable self-assembly of smart, digital, and structurally complex materials from simple components at size scales from the macro to the nano remains a long-standing goal of material science. Here, we introduce a platform based on magnetic encoding of information to drive programmable self-assembly that works across length scales. Our building blocks consist of panels with different patterns of magnetic dipoles that are capable of specific binding. Because the ratios of the different panel-binding energies are scale-invariant, this approach can, in principle, be applied down to the nanometer scale. Using a centimeter-sized version of these panels, we demonstrate 3 canonical hallmarks of assembly: controlled polymerization of individual building blocks; assembly of 1-dimensional strands made of panels connected by elastic backbones into secondary structures; and hierarchical assembly of 2-dimensional nets into 3-dimensional objects. We envision that magnetic encoding of assembly instructions into primary structures of panels, strands, and nets will lead to the formation of secondary and even tertiary structures that transmit information, act as mechanical elements, or function as machines on scales ranging from the nano to the macro.

Elastic backbone phase transition in the Ising model.

The two-dimensional (zero magnetic field) Ising model is known to undergo a second-order paraferromagnetic phase transition, which is accompanied by a correlated percolation transition for the Fortuin-Kasteleyn (FK) clusters. In this paper we uncover that there exists also a second temperature T_{eb}<T_{c} at which the elastic backbone of FK clusters undergoes a second-order phase transition to a dense phase. The corresponding universality class, which is characterized by determining various percolation exponents, is shown to be completely different from directed percolation, which leads us to propose a new anisotropic universality class with β=0.54±0.02, ν_{||}=1.86±0.01, ν_{⊥}=1.21±0.04, and d_{f}=1.53±0.03. All tested hyperscaling relations are shown to be valid.

Steering a Multi-armed Robotic Sheath Using Eccentric Precurved Tubes.

This paper presents a novel continuum robot sheath for use in single-port minimally invasive procedures such as neuroendoscopy in which the sheath is designed to deliver multiple robotic arms. Articulation of the sheath is achieved by using precurved superelastic tubes lining the working channels used for arm delivery. These tubes perform a similar role to push/pull tendons, but can accomplish shape change of the sheath via rotation as well as translation. A kinematic model using Cosserat rod theory is derived which is based on modeling the system as a set of eccentrically aligned precurved tubes constrained along their length by an elastic backbone. The specific case of a two-arm sheath is considered in detail and its relationship to a concentric tube balanced pair is described. Simulation and experiment are used to investigate the concept, map its workspace and to evaluate the kinematic model.

Injectable polyphosphazene/gelatin hybrid hydrogel for biomedical applications

Injectable hydrogels are promising candidates for tissue engineering because of their easy and minimally invasive manipulation, and their ability to mimic the features of the extracellular matrix. Hydrogels developed from water-soluble polyphosphazenes are attractive due to the unique flexibility of phosphazene chemistry. In this study, a photocrosslinkable water-soluble polyphosphazene was synthesized by introducing citronellol with a double bond and hydrophilic diethylene glycol monomethyl ether as cosubstituted side groups; the corresponding hydrogel was obtained by exposing the polyphosphazene aqueous solution to ultraviolet light. Benefiting from the elastic polyphosphazene backbone and the flexible ether side group, the hydrogel exhibited excellent injectability and mechanical stability. To improve the hydrogel's mechanical and biological properties targeting biomedical applications, photocrosslinkable methacrylate gelatin and inorganic calcium phosphate were incorporated. The resulting composite hydrogels were able to retain excellent injectability, deformability and fatigue resistance, and were evaluated to be excellent for biomedical applications via in vitro cell culture and in vivo subcutaneous implantation.

Robust control of continuum robots using Cosserat rod theory

In this paper we introduce the first robust control for continuum robots that are modelled by Cosserat Rod theory. Constituted from deformable elastic backbones, continuum robots are highly nonlinear and complex. Current control approaches tend to overcome this obstacle by adopting assumptions to the robot’s structure aiming to develop models that are both accurate and applicable for real time control applications. The drawback of such approaches is that maintaining those modelling assumptions restricts the robots expected performance. Here, we overcome the drawbacks by utilizing a dynamic model based on Cosserat Rod that is free from those assumptions and capable of accommodating the backbone general deformations. This general model has not been used in robust control design before as it is computationally expensive to simulate and be used for real time control applications. In this paper, we solved the expensive computation problem by employing a sophisticated numerical method known as the Generalized-α method. For the control part, a robust controller is designed based on sliding mode. To avoid drastic changes in the actuating tension, control input saturation is considered in the design process. Simulation examples are included to verify the effectiveness of the proposed design.

Elastic Backbone Defines a New Transition in the Percolation Model.

The elastic backbone is the set of all shortest paths. We found a new phase transition at p_{eb} above the classical percolation threshold at which the elastic backbone becomes dense. At this transition in 2D, its fractal dimension is 1.750±0.003, and one obtains a novel set of critical exponents β_{eb}=0.50±0.02, γ_{eb}=1.97±0.05, and ν_{eb}=2.00±0.02, fulfilling consistent critical scaling laws. Interestingly, however, the hyperscaling relation is violated. Using Binder's cumulant, we determine, with high precision, the critical probabilities p_{eb} for the triangular and tilted square lattice for site and bond percolation. This transition describes a sudden rigidification as a function of density when stretching a damaged tissue.