Elastic Chain Research Articles

Multi-degenerate hill-top bifurcation of Fermi–Pasta–Ulam softening chains: Exact and asymptotic solutions

A one-dimensional nonlinear elastic chain, known as Fermi–Pasta–Ulam system, is analyzed in the static field. The chain is made of elements admitting a quartic potential, with softening nonlinear behavior. When the chain is subject to pure tension, it exhibits a multi-degenerate hill-top bifurcation, from which several softening branches bifurcate. On each path, the springs either behave softening or hardening, in all the possible combinations, making the response non-unique. Both exact and asymptotic solutions are pursued, and the multitude of the bifurcated paths is illustrated by bifurcation diagrams. A proof of their instability is given. The role of the imperfections is commented, either in modifying the equilibrium paths and in unfolding the degenerate bifurcation.

Periodontal status following orthodontic mini-screw insertion: A prospective clinical split-mouth study.

Anchorage control is one of the most important determinants of orthodontic treatments. Mini-screws are used to achieve the desired anchorage. Despite all their advantages, there is a possibility that treatment will not be successful due to conditions related to their interaction with the periodontal tissue. To evaluate the status of the periodontal tissue at the sites adjacent to the orthodontic mini-implants. A total of 34 teeth (17 case and 17 control) in 17 orthodontic patients requiring a mini-screw in the buccal area to proceed with their treatment were included in the study. Oral health instruction was provided to the patients prior to the intervention. In addition, scaling and root planing of the root surface were done using manual instruments and ultrasonic instruments if needed. For tooth anchorage, a mini-screw with Elastic Chain or Coil Spring was used. The following periodontal indices were examined in the mini-screw receiving tooth and the contralateral tooth: plaque index, pocket probing depth, attached gingiva level (AG), and gingival index. Measurements were made before the placement of the mini-screws and 1, 2, and 3 months following that. The results revealed a significant difference only in the amount of AG between the tooth with mini-screw and the control tooth (p = 0.028); for other periodontal indices, there were no significant differences between the two groups. This study showed that periodontal indices in adjacent teeth of the mini-screws do not change significantly compared to other teeth and mini-screws can be used as a suitable anchorage without posing a threat to the periodontal health. Using mini-screws is a safe intervention for orthodontic treatments.

Ambient-conditions spinning of functional soft fibers via engineering molecular chain networks and phase separation

Producing functional soft fibers via existing spinning methods is environmentally and economically costly due to the complexity of spinning equipment, involvement of copious solvents, intensive consumption of energy, and multi-step pre-/post-spinning treatments. We report a nonsolvent vapor-induced phase separation spinning approach under ambient conditions, which resembles the native spider silk fibrillation. It is enabled by the optimal rheological properties of dopes via engineering silver-coordinated molecular chain interactions and autonomous phase transition due to the nonsolvent vapor-induced phase separation effect. Fiber fibrillation under ambient conditions using a polyacrylonitrile-silver ion dope is demonstrated, along with detailed elucidations on tuning dope spinnability through rheological analysis. The obtained fibers are mechanically soft, stretchable, and electrically conductive, benefiting from elastic molecular chain networks via silver-based coordination complexes and in-situ reduced silver nanoparticles. Particularly, these fibers can be configured as wearable electronics for self-sensing and self-powering applications. Our ambient-conditions spinning approach provides a platform to create functional soft fibers with unified mechanical and electrical properties at a two-to-three order of magnitude less energy cost under ambient conditions.

Highly Stretchable and Flexible Electrospinning‐Based Biofuel Cell for Implantable Electronic

AbstractWith the emerging demand of implantable microelectronics, it essentially requires the fully integrated and reliable power supplies. The study reports a stretchable and flexible electrospinning‐based glucose/O2 biofuel cell with glucose oxidase bioanode, Pt/C cathode and thermoplastic polyurethane substrate, which is capable for adapting to the various stresses and strains caused by individual movement. The rigid benzene rings and elastic chain segments of thermoplastic polyurethane ensure its superior tensile property. Furthermore, the stable covalent connections between the activated carbon nanotubes (CNTs‐COOH) and glucose oxidase inside 3D thermoplastic polyurethane network are established by amide reaction to ensure the rapid direct electron transfer of bioanode and stable power output of device in flexible environments. The biofuel cell exhibits an open circuit voltage of 0.575 V, and high‐power density of 57 µW cm−2 in 5 mM glucose. Moreover, the power‐generation properties of implantable biofuel cell keep steady, and its power density exhibits limited fluctuations on the dorsum of rat when bending, stretching, and twisting in 28 days. There is no obvious local inflammation or systemic abnormalities in rats. It satisfies the impressive biocompatible requirement, demonstrating the promising potential of electrospinning‐based biofuel cell as a robust self‐sustained power source for implantable electronics.

Seven-Week Accommodating Resistance Training Improves Wingate Peak Power But Not Muscular Strength or Endurance in Strength-Trained Females.

Parten, AL, Barker, GA, O'Neal, EK, and Waldman, HS. Seven-week accommodating resistance training improves Wingate peak power but not muscular strength or endurance in strength-trained females. J Strength Cond Res 37(9): 1789-1794, 2023-Accommodating resistance (AR) is a training technique that includes attaching elastic bands or chains to a loaded barbell to alter the resistance profile throughout the barbell movement. This study was the first to quantify the effects of AR versus a traditional resistance (TR) training program on changes in strength and power profiles in a trained female cohort. Resistance-trained (training history: 2.4 ± 1.4 years) females (age: 22.1 ± 3.0 years) completed baseline and postintervention tasks which included 1 repetition maximum (1RM) testing in the back squat (BS) and bench press (BP), a repetitions to failure in the BP (60% of 1RM), and 1 30-s Wingate test. After baseline testing, subjects were stratified (based on relative strength) into either the AR ( n = 9) or TR ( n = 10) group and then completed a supervised, 7-week training intervention. Both groups improved their 1RM in both lifts, but no statistical differences were found between groups in 1RM for BS, BP, or BP to failure ( p > 0.05). However, the AR group increased Wingate peak power (837 ± 221 to 901 ± 215 W; p = 0.04), whereas TR (868 ± 244 to 8,343 ± 182 W; p = 0.47) did not. This study supports AR with lighter relative barbell load incurs similar strength adaptations as TR. For coaches training athletes concerned with power, AR may be advantageous for improving rate of force development as demonstrated by large increases in peak Wingate power.

A multiscale phase field fracture approach based on the non-affine microsphere model for rubber-like materials

Rubber-like materials have a broad scope of applications due to their unique properties like high stretchability and increased toughness. Hence, computational models for simulating their fracture behavior are paramount for designing them against failures. In this study, the phase field fracture approach is integrated with a multiscale polymer model for predicting the fracture behavior in elastomers. At the microscale, damaged polymer chains are modeled to be made up of a number of elastic chain segments pinned together. Using the phase field approach, the damage in the chains is represented using a continuous variable. Both the bond stretch internal energy and the entropic free energy of the chain are assumed to drive the damage, and the advantages of this assumption are expounded. A framework for utilizing the non-affine microsphere model for damaged systems is proposed by considering the minimization of a hypothetical undamaged free energy, ultimately connecting the chain stretch to the macroscale deformation gradient. At the macroscale, a thermodynamically consistent formulation is derived in which the total dissipation is assumed to be mainly due to the rupture of molecular bonds. Using a monolithic scheme, the proposed model is numerically implemented and the resulting three-dimensional simulation predictions are compared with existing experimental data. The capability of the model to qualitatively predict the propagation of complex crack paths and quantitatively estimate the overall fracture behavior is verified. Additionally, the effect of the length scale parameter on the predicted fracture behavior is studied for an inhomogeneous system.

Multidisciplinary approach to restore esthetics and function in a young patient with three consecutive impacted teeth: a case report with 18-month follow-up.

This case report describes the orthodontic treatment of an 11-year-old patient with three maxillary impacted teeth on the right side. Cone-beam computed tomography showed that these teeth were close together, with the lateral incisor in a lower position, followed by the central incisor, and the canine in a more apical position. Treatment included applying traction to these teeth. A transpalatal arch was used as an anchorage device, and surgical exposure of the lateral incisor was performed for traction with an elastic chain toward the hook welded to the 0.017 × 0.025-inch steel segmented arch. Subsequently, the central incisor was surgically exposed, elastic chains were used, along with a 0.016-inch steel arch with a box loop for correcting the tooth position. The canine spontaneously began to erupt, and a 0.017 × 0.025-inch TMA segmented arch with boot loop was used to control rotation and torque of the canine during its distalization. Once these three teeth were in the arch, treatment was finished in the usual manner. For esthetic improvement, gingivoplasty was performed in the maxillary arch. Eighteen-month follow-up showed that orthodontic treatment allowed preservation of the natural teeth, the contour of gingival support, and avoidance of prosthetic rehabilitation, reestablishing the patient's esthetics and function, with satisfactory stability.

Morphology, Micromechanical, and Macromechanical Properties of Novel Waterborne Poly(urethane-urea)/Silica Nanocomposites.

Morphology, macro-, and micromechanical properties of novel poly(urethane-urea)/silica nanocomposites were analyzed by electron microscopy, dynamic mechanical thermal analysis, and microindentation. The studied nanocomposites were based on a poly(urethane-urea) (PUU) matrix filled by nanosilica, and were prepared from waterborne dispersions of PUU (latex) and SiO2. The loading of nano-SiO2 was varied between 0 (neat matrix) and 40 wt% in the dry nanocomposite. The prepared materials were all formally in the rubbery state at room temperature, but they displayed complex elastoviscoplastic behavior, spanning from stiffer elastomeric type to semi-glassy. Because of the employed rigid and highly uniform spherical nanofiller, the materials are of great interest for model microindentation studies. Additionally, because of the polycarbonate-type elastic chains of the PUU matrix, hydrogen bonding in the studied nanocomposites was expected to be rich and diverse, ranging from very strong to weak. In micro- and macromechanical tests, all the elasticity-related properties correlated very strongly. The relations among the properties that related to energy dissipation were complex, and were highly affected by the existence of hydrogen bonding of broadly varied strength, by the distribution patterns of the fine nanofiller, as well as by the eventual locally endured larger deformations during the tests, and the tendency of the materials to cold flow.

Effect of filament types and loops number on the force degradation of elastomeric chains used for orthodontic treatment: an in-vitro study

BackgroundIn orthodontic treatment, closing spaces, specifically the extraction and scattered spaces of the anterior teeth, requires some auxiliary bias, such as an elastomeric chain. Many factors affect the mechanical properties of elastic chains. In this study, we investigated the relationship of the filament type, the number of loops, and the force degradation of elastomeric chains under thermal cycling conditions.MethodsThe orthogonal design included three filament types (i.e., close, medium, and long). Four, five, and six loops of each elastomeric chain were stretched to have an initial force of 250 g in an artificial saliva environment at 37 °C and thermocycling between 5 and 55 °C three times a day. The remaining force of the elastomeric chains was recorded at different time points (4 h, 24 h, 7 days, 14 days, 21 days, and 28 days), and the percentage of the remaining force was calculated.ResultsThe force decreased significantly in the initial 4 h and degraded mostly within the first 24 h. In addition, the percentage of force degradation increased slightly between 1 and 28 days.ConclusionsUnder the same initial force, the longer the connecting body is, the fewer the number of loops and the greater the force degradation of the elastomeric chain are.

Impact Buffering Characteristics of One-Dimensional Elastic-Plastic Composite Granular Chain.

Considering the elastic-plastic deformation, the wave propagations and energy transmissions of the one-dimensional three-segment composite granular chain are studied. The axial symmetry model for elastic-perfectly plastic materials is built by using the finite element method. Six materials with different yield strengths are selected for the adjustable segment. The results show that the repeated loading and unloading behaviors, as well as the wave propagations in the elastic-plastic granular chain, are complex and significantly different from those in the purely elastic granular chain. The yield strength of the granular materials in the adjustable segment has significant effects on energy dissipation and wave velocity, which could be used to design the impact buffer. The studies show that taking lower yield strength for the adjustable part than the non-adjustable part, the energy dissipation could be increased, and the wave velocity could be reduced, then the arrival time of the impact waves could be delayed. These characteristics of the elastic-plastic granular chain could be used to design metamaterials for impact absorbers in impact protection.

Finite Element Study to Evaluate the Stress Around Mini-implant during Canine Retraction using Continuous and Interrupted Orthodontic Forces

Abstract:
 Objectives: This work aimed to determine the stress distribution around a mini-implant during dynamic canine retraction utilizing continuous and intermittent orthodontic forces and a three-dimensional finite element model.
 Materials and Methods: Establishing a three-dimensional finite element model of canine retraction. The model incorporates a mini-implant, alveolar bone, maxillary teeth, a closed coil spring, and an elastic chain. They were described as being homogeneous, isotropic, and linear elastic. Continuous and interrupted forces were approximated by a NiTi coil spring and an elastic chain, respectively. To retract the canine, a simulated orthodontic force of 1.5N, 2N, and 2.5N were loaded. ANSYS evaluated the value of the stress distribution around the mini-implant, canine, and bone interface (workbench 19).
 Results indicated that there was no significant difference between the values of maximum stress around the miniscrew, canine, and bone under different orthodontic loads when a closed coil spring and an elastic chain were evaluated.

Design, numerical simulation and in vitro examination of a CAD/CAM fabricated active orthodontic treatment element.

Orthodontic treatments with custom-made active elements may lead to more efficient treatment with fewer side effects. The objective of this in vitro study was to determine whether individually constructed, mathematically simulated and 3D printed power chains can generate adequate forces for orthodontic tooth movement. An individual measurement device was developed using a high precision load cell, amplifier and microcontroller for signal processing. Elastic chains were designed and subsequently printed from two different thermoplastic Polyurethan (TPU) filaments and thermoplastic elastomer (TPE) filament. With the CAD-data a finite elemente analysis (FEA) was performed to calculate the reactive forces to be expected at different activation levels. The measured force development of the test objects was compared with the results from the FEA. The results showed a high precision of the measurement device with ICC of 0.999 and a Dahlberg error of 0.05 N. The measured forces ranged from 168 g to 680 g. There was a significant correlation between measured and calculated forces (R 0.91 to 0.98). In this study, the fully digital workflow of producing an individualized active orthodontic treatment element, which developed almost exactly the force values calculated in the FEA, was shown. Future clinical use seems promising in combination with fully individualized and digitally planned treatment approaches. This offers the possibility to integrate these insights from examplary applications into patient-specific digital planning in orthodontics. The combination of CBCT root reconstruction, intraoral scans with customized brackets, and wires is the perfect starting point to add mechanical and numerical simulations. This would be the next step from shape driven planning to force driven planning. The goal is to reduce treatment time and negative side effects, e.g., root resorption. This in vitro study is the first to show the possible individualized construction and 3D printing of elastic chains exhibiting reproducible, predefined forces.

Repositioning of Impacted Canine Using Elastic Chain

Repositioning of Impacted Canine Using Elastic Chain

Force behaviour of elastic chains during a simulated gap closure in extraction therapy cases.

Tooth movement with elastic chains requires defined force magnitudes. This study assessed the force behaviour of different elastic chains at different configurations of gap width. Self-ligating brackets of teeth 5 & 6 and 2 & 3 were bonded to two movable aluminium plates. The plates were positioned on a joint basis with varying distances of 0.5, 2.0, 4.0, 6.0, and 8.0 mm. Reset forces of open and closed chains from four different manufacturers were investigated in four different configurations. Configurations differed in either having an additional intermediate ring within the gap (#1, #3) and/or having intermediate rings between teeth adjacent to the gap (#1, #2), or by no intermediate rings (#4). Forces were measured with a universal testing machine. The results were statistically analysed using U-test, H-test and (if applicable) post-hoc tests with a significance level of .05. Configurations #1 and #3, and #2 and #4 formed homogenous subgroups (P < .001). Initial forces in configuration #4 were significantly higher than in configuration #3 (P=.029). Initial forces in closed chains were significantly higher than for open chains (P=.029). Intermediate chain rings adjacent to the gap are not required to modulate the force. In contrast, leaving a ring unapplied in the tooth gap can help modulate the force. Open thermoset chains with an additional ring within the gap (#3) seem to produce suitable initial forces for a gap closure of 4 mm. With a residual gap width of <2 mm, open thermoset chains and closed thermoset chains (#4) seem suitable.

Dynamic fracture regimes forinitially prestressed elastic chains.

We study the propagation of a bridge crack in an anisotropic multi-scale system involving two discrete elastic chains that are interconnected by links and possess periodically distributed inertia. The bridge crack is represented by the destruction of every other link between the two elastic chains, and this occurs with a uniform speed. This process is assumed to be sustained by energy provided to the system through its initial configuration, corresponding to the alternating application of compression and tension to neighbouring links. The solution, based on the Wiener–Hopf technique and presented in Ayzenberg-Stepanenko et al. (Ayzenberg-Stepanenko et al. 2014 Proc. R. Soc. A 470, 20140121 (doi:10.1098/rspa.2014.0121)) is used to compute the profile of the medium undergoing failure. We investigate when this solution, representing the steady failure process, is physically acceptable. It is shown that the analytical solution is not always physically applicable and can be used to determine the onset of non-steady failure regimes. These arise from the presence of critical deformations in the wake of the crack front at the sites of the intact links. Additionally, we demonstrate that the structural integrity of the discrete elastic chains can significantly alter the range of speeds for which the bridge crack can propagate steadily.This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’.

Efficiency of different miniscrew positions for maxillary incisor intrusion: A comparative cone beam study

Aim: To evaluate the treatment efficacy of two different position of mini-implant-assisted methods to intrude the maxillary incisors using cone-beam computed tomography (CBCT). Patients and Methods: The study included 26 patients with elongated maxillary incisors and a deep bite, ranging in age from 12 to 18 years. One group received anterior mini-implants, whereas the other received posterior ones at random. The AMG used elastic chains to apply about 40 g of force per side, while the PMG used beta-titanium wires. This investigation used CBCT scans that were performed before and after an intrusion that lasted 18 weeks. Result: Significant changes in the labial inclination of all incisors, which were greater in PMG than AMG. Conclusion: Both mechanics result in increased labial tilting, but posterior mini-implants assisted maxillary incisor intrusion is greater, so it is preferred when the patient's incisors is upright position.

Different Methods of Canine Retraction- Part 1

Background: This review aimed at explaining different methods of canine retraction along the archwire. Methods: Searching for different methods of canine retraction using fixed orthodontic appliances was carried out using different databases, including PubMed Central, Science Direct, Wiley Online Library, the Cochrane Library, Textbooks, Google Scholar, Research Gate, and hand searching from 1930 till February 2022. Results: After excluding the duplicate articles, papers describing the methods of canine retraction along the archwires were included. The most commonly used methods are NiTi closed coil spring and elastic chain. Conclusions: Various methods of canine retraction along the archwires were explained in detail regarding their advantages, disadvantages, and comparisons among different methods supported by clinical trials, systematic review, and meta-analysis. The preferred method is canine retraction with NiTi closed coil spring with 150 and 200 gm. Elastic chain is considered an alternative, low-cost option.

Effects of Mandibular Canine Intrusion Obtained Using Cantilever Versus Bone Anchorage: A Comparative Finite Element Study.

BackgroundThis study was conducted to assess and compare the effects of mandibular canine intrusion obtained using a cantilever having different toe-in bends and with mini-implants using the three-dimensional (3D) finite element method (FEM).Methodology3D models of the mandibular right quadrant were created using FEM. Brackets and molar tubes were also modeled. In the first model, the mandibular canine intrusion was produced using a cantilever loop with compensatory toe-in bends (0°, 4°, 6°, and 8°). In another model, the intrusion was done using two mini-implants. Force was applied using an elastic chain. The amount of intrusion and the associated labial tipping of canine that occurred in both the models was assessed and compared using FEM analysis.ResultsThe pure intrusion of the canine was produced by the 6° toe-in bend of the cantilever. The labial tipping of the canine was also reduced. The highest amount of periodontal ligament stress was observed around the canine root with a 0° toe-in bend. In the posterior segment, the molar displayed a slight tendency for extrusion and distal crown tipping.ConclusionsThe intrusion mechanics using a cantilever simulated in this study may achieve pure mandibular canine intrusion with minimal labial tipping when a compensatory toe-in of 6° is incorporated into the cantilever.

Prestrain-induced contraction in one-dimensional random elastic chains

Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. Motivated by this observation, we here consider a minimal model in one dimension to set the stage for understanding the response of such networks as a function of the prestrain. To this end we consider a chain [one-dimensional (1D) network] of elastic springs upon which a random, zero mean, finite variance prestrain is imposed. Numerical simulations and analytical predictions quantify the magnitude of the contraction as a function of the variance of the prestrain, and show that the chain always shrinks. To test these predictions, we vary the topology of the chain, consider more complex connectivity and show that our results are relatively robust to these changes.

Chiral waves in structured elastic systems: dynamics of a meta-waveguide

Summary The notion of meta-surfaces is well established for waves interacting with arrays of periodic resonators. Here, an infinite elastic rod, attached to a system of gyroscopic spinners, is considered. This forms a waveguide with unusual dispersion properties and will be referred to as a chiral meta-waveguide. A class of transient and time-harmonic formulations describing waves in elastic chiral meta-waveguides is addressed. Consideration of a chiral elastic chain leads to the governing equations of the homogenised continuous system. Both analytical and numerical solutions are presented. Features observed for chiral waveforms show resemblance with formulations of quantum physics rather than linear elasticity. For an elementary example related to an elastic chiral rod, with the absence of pre-tension, it is noted that the longitudinal velocity satisfies the Klein–Gordon equation. For full vector problems, corresponding to an elastic chiral rod with pre-tension, time-harmonic Green’s matrix functions are derived for the case of large values of the gyricity parameter. This case is especially interesting because of the presence of both exponentially localised and oscillatory terms in the representation of Green’s matrix components.