Spring Chain Research Articles

Continuum limits of bistable spring models of carbon nanotube arrays accounting for material damage

Using chains of bistable springs, a model is derived to investigate the plastic behavior of carbon nanotube arrays with damage. We study the preconditioning effect due to the loading history by computing analytically the stress–strain pattern corresponding to a fatigue-type damage of the structure. We identify the convergence of the discrete response to the limiting case of infinitely many springs, both analytically in the framework of Gamma-convergence, as well as numerically.

Two nonlinear compactness theorems in Lp(0,T;B)

We establish two nonlinear compactness theorems in L p ( 0 , T ; B ) with hypothesis on time translations, which are nonlinear counterparts of two results by Simon (1987) [1] . The first theorem sharpens a result by Maitre (2003) [10] and is important in the study of doubly nonlinear elliptic–parabolic equations. Based on this theorem, we then obtain a time translation counterpart of a result by Dubinskii˘ (1965) [5] , which is supposed to be useful in the study of some nonlinear kinetic equations (e.g. the FENE-type bead–spring chains model).

Single-file diffusion of particles in a box: Transient behaviors

We consider a finite number of particles with soft-core interactions, subjected to thermal fluctuations and confined in a box with excluded mutual passage. Using numerical simulations, we focus on the influence of the longitudinal confinement on the transient behavior of the longitudinal mean squared displacement. We exhibit several power laws for its time evolution according to the confinement range and to the rank of the particle in the file. We model the fluctuations of the particles as those of a chain of springs and point masses in a thermal bath. Our main conclusion is that actual system dynamics can be described in terms of the normal oscillation modes of this chain. Moreover, we obtain complete expressions for the physical observables, in excellent agreement with our simulations. The correct power laws for the time dependency of the mean squared displacement in the various regimes are recovered, and analytical expressions of the prefactors according to the relevant parameters are given.

Sedimentation of a sphere in a viscoelastic fluid: a multiscale simulation approach

AbstractA long-standing problem in non-Newtonian fluid mechanics, namely the relationship between drag experienced by a sphere settling in a tube filled with a dilute polymeric solution and the sphere sedimentation velocity, is investigated via self-consistent multiscale flow simulations. Comparison with experimental measurements by Arigo et al. (J. Non-Newtonian Fluid Mech., vol. 60, 1995, pp. 225–257) have revealed that the evolution of the drag coefficient as a function of fluid elasticity can be accurately predicted when the macromolecular dynamics is described by realistic micromechanical models that closely capture the transient extensional viscosity of the experimental fluid at high extension rates. Specifically, for the first time we have computed the drag coefficient on the sphere at high Weissenberg number $\mathit{Wi}$ utilizing multi-segment bead–spring chain models with appropriate molecular parameters and have demonstrated that a hi-fidelity multiscale simulation is not only capable of accurately describing the drag on the sphere as a function of $\mathit{Wi}$ at various sphere-to-tube diameter ratios but also it can closely reproduce the experimentally observed velocity and stresses in the wake of the sphere.

The influence of viscosity on the response of open-cell polymeric foams in uniaxial compression: experiments and theoretical model

In a preceding paper (Pampolini and Del Piero in J Mech Mater Struct 3:969–981, 2008), the response of blocks made of a polymeric open-cell foam subject to uniaxial compression was analyzed. The hysteretic behavior exhibited in cyclic tests was interpreted within the context of nonlinear elasticity, as an effect of strain localization due to the non-convexity of the energy. Here we study some inelastic aspects of the response, such as rate dependence, strength decay after repeated loading, and memory effects. The analysis of some key experiments led us to the conclusion that viscous effects prevail over plasticity and damage. Consequently, we propose here a visco-elastic model, obtained by adding linear visco-elastic elements to our previous chain of nonlinear elastic springs. The paper is completed by the description of a series of experiments and of numerical simulations.

Teaching wave propagation and the emergence of Viète’s**The Latin version of this French name is usually quoted as Vieta. formula

The well-known result for the frequency of a simple spring–masssystem may be combined with elementary concepts like speed = wavelength × frequency to obtain wave propagation speeds for an infinite chain of springs and masses (masses m held apart atequilibrium distance a by springs of stiffness γ). These propagation speeds are dependent on the wavelength of the wave. The dispersionis easily investigated by considering normal modes of increasing wavelength. Thisinvestigation also elegantly highlights how the dispersion physically arises in the form of effective spring constants due to the way in which neighbouring springs contribute tothe propagation of each of the normal modes. The resulting propagation speeds v(λ) are given by an expression , which in the limit of large λ becomes . This of course means that —the serendipitous emergence of what turns out to be Viète’s formula forπ in terms of nested roots of 2.

Dynamic Structure Factor for Large Aggregate Clusters with Internal Motions: A Self-Consistent Light-Scattering Study on Conjugated Polymer Solutions

The aggregation properties of a standard conjugated polymer, poly(2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylenevinylene) (MEH-PPV), in two distinct solvents (chloroform and toluene) and a range of polymer concentrations (c = 0.1-3 mg/mL) have been unequivocally resolved using combined dynamic and static light scatterings (DLS/SLS). The prime challenges for analyzing this peculiar, practically important, solution system arise from the wide size distribution and unknown aggregate morphology, as well as pronounced interferences between translational and internal motions of aggregate clusters of considerably varying size. To cope with these central difficulties, we propose a self-consistent formulation for analyzing the dynamic structure factor in DLS experiment by extending an existing theory on free-draining bead-spring chains that explicitly accounts for internal fluctuations, along with two candidate form factors on Gaussian coil and rigid sphere, respectively, serving as two limiting cases to be discriminated in combined DLS and SLS measurements. Given that no accessibility to ultrasmall angular resolutions is a prerequisite, the suggested protocol can readily be carried out in conventional light-scattering apparatus. The present analyses unanimously support the rigid-sphere form factor in describing the entire set of light-scattering data on MEH-PPV solutions, differing from early small-angle neutron/X-ray scattering interpretations suggesting certain 2D fractal structures for the aggregation network. Scrutiny into the interior dynamics of aggregate clusters further disclosed that the segmental motions are noticeably more suppressed than for usual, nonaggregated polymer solutions, and no existing theories based on the bead-spring picture can yet capture the observed scaling behavior as manifested by the present data. Accordingly, we report several first-revealed properties of MEH-PPV solutions on the aggregate morphology, the size distribution (and mean size), mean aggregation number, and interior segmental dynamics, which serve as valuable information for linking solution properties with those for dried thin films in contemporary applications with conducting conjugated polymers.

Evaluation of space closure rate during canine retraction with nickel titanium closed coil spring and elastomeric chain.

Aims: . To investigate the rates of space closure achieved by elastomeric chain and nickel titanium coil springs with the evaluation of the effects of using different bracket types on the rate of space closure during its retraction along different sizes of orthodontic arch wires using typodont simulation system (Ormco). Materials and Methods: The standardization criteria were all typodont teeth situated in well aligned position, covered and immobilized by the acrylic bite except canine, elastic chain and nickel – titanium closed coil spring exerting 180 gm of force on canine measured carefully by tension gauge. The available space was 13.5mm (the rate of space closure). Results: The present study showed that when using elastic chain as a method of canine retraction gave rise to a a significant decrease in the rate of space closure as compared with nickel – titanium closed coil spring also sliding the canine using ceramic brackets gave rise significant reduction in the rate of space closure than when using stainless steel brackets. Another finding of the present study showed that sliding the canine on large rectangular arch wire (0.019x0.025 inch) gave rise to a significant reduction in the rate of space closure when com-pared with 0.018 inch and 0.018x0.022 inch arch wires were used. Conclusions: It was concluded that the canine retraction with 0.018 inch wire on Roth stainless steel bracket by closed coil spring gave rise a large amount of space closure rate. While the opposite is true for canine retraction with 0.019x0.025 inch wire on standard ceramic bracket by elastic chain retraction method.

Polyelectrolytes in Salt Solutions: Molecular Dynamics Simulations

We present results of the molecular dynamics simulations of salt solutions of polyelectrolyte chains with number of monomers N = 300. Polyelectrolyte solutions are modeled as an ensemble of bead–spring chains of charged Lennard-Jones particles with explicit counterions and salt ions. Our simulations show that in dilute and semidilute polyelectrolyte solutions the electrostatic induced chain persistence length scales with the solution ionic strength as I–1/2. This dependence of the chain persistence length is due to counterion condensation on the polymer backbone. In dilute polyelectrolyte solutions the chain size decreases with increasing the salt concentration as R ∝ I–1/5. This is in agreement with the scaling of the chain persistence length on the solution ionic strength, lp ∝ I–1/2. In semidilute solution regime at low salt concentrations the chain size decreases with increasing polymer concentration, R ∝ cp–1/4, while at high salt concentrations we observed a weaker dependence of the chain size on th...

Dynamics of enzymatic digestion of elastic fibers and networks under tension

We study the enzymatic degradation of an elastic fiber under tension using an anisotropic random-walk model coupled with binding-unbinding reactions that weaken the fiber. The fiber is represented by a chain of elastic springs in series along which enzyme molecules can diffuse. Numerical simulations show that the fiber stiffness decreases exponentially with two distinct regimes. The time constant of the first regime decreases with increasing tension. Using a mean field calculation, we partition the time constant into geometrical, chemical and externally controllable factors, which is corroborated by the simulations. We incorporate the fiber model into a multiscale network model of the extracellular matrix and find that network effects do not mask the exponential decay of stiffness at the fiber level. To test these predictions, we measure the force relaxation of elastin sheets stretched to 20% uniaxial strain in the presence of elastase. The decay of force is exponential and the time constant is proportional to the inverse of enzyme concentration in agreement with model predictions. Furthermore, the fragment mass released into the bath during digestion is linearly related to enzyme concentration that is also borne out in the model. We conclude that in the complex extracellular matrix, feedback between the local rate of fiber digestion and the force the fiber carries acts to attenuate any spatial heterogeneity of digestion such that molecular processes manifest directly at the macroscale. Our findings can help better understand remodeling processes during development or in disease in which enzyme concentrations and/or mechanical forces become abnormal.

物体投擲のためのねじりばねの直列構造に基づく瞬発力発生装置

In this paper, we propose an impulse force generator for catapulting an object. The proposed impulse force generator utilizes snap-through buckling of an elastic body. The distinguished feature of the device is to adopt a serial chain of torsion springs with both high elasticity and flexibility as its elastic body. The use of the serial chain of torsion springs enables us to increase the energy density of the elastic body. Experimental results show that the proposed compact and lightweight impulse force generator has high capability of catapulting an object. The generated maximum momentum is of 16[Ns] in spite that the maximum driving torque necessary for snap-through buckling is only of 21[Nm].

Simulating the Relaxation of Stretched DNA in Slitlike Confinement

Brownian dynamics simulations of bead−spring chains were used to study the relaxation of an initially stretched DNA molecule in slitlike confinement. Taking into account excluded volume effects but...

WITHDRAWN: A mixed Brownian dynamics—SPH method for the simulation of flows of suspensions of bead–spring chains in confined geometries with hydrodynamic interaction

This article has been withdrawn at the request of the author(s) and/or editor. The Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.

Effect of Solvent Quality on the Coil−Stretch Transition

Polymers undergo a sharp coil−stretch transition in extension dominated flows when the strain rate exceeds a critical strain rate. We investigate this transition in both Θ solvents and good solvents using Brownian dynamics simulations. The polymer is represented by a bead−spring chain model undergoing elongational flow and solvent-mediated effects such as fluctuating hydrodynamic interactions (HI) and excluded volume (EV) are included rigorously. A 1-D energy landscape theory with an activation energy for transition(1) is used to gain qualitative insights into the dynamics. A key factor in determining the influence of solvent quality is the use of a proper measure of solvent quality.(2, 3) Contrary to earlier findings, it is observed that with improvement in solvent quality, the critical strain rate at which the coil to stretch transition takes place decreases. Furthermore, the solvent quality has a profound effect on the scaling of the critical strain rate with molecular weight and on both the transient ...

Multiscale mass-spring models of carbon nanotube foams

This article is concerned with the mechanical properties of dense, vertically aligned CNT foams subject to one-dimensional compressive loading. We develop a discrete model directly inspired by the micromechanical response reported experimentally for CNT foams, where infinitesimal portions of the tubes are represented by collections of uniform bi-stable springs. Under cyclic loading, the given model predicts an initial elastic deformation, a non-homogeneous buckling regime, and a densification response, accompanied by a hysteretic unloading path. We compute the dynamic dissipation of such a model through an analytic approach. The continuum limit of the microscopic spring chain defines a mesoscopic dissipative element (micro–meso transition) which represents a finite portion of the foam thickness. An upper-scale model formed by a chain of non-uniform mesoscopic springs is employed to describe the entire CNT foam. A numerical approximation illustrates the main features of the proposed multiscale approach. Available experimental results on the compressive response of CNT foams are fitted with excellent agreement.

Multiple scales analysis of wave–wave interactions in a cubically nonlinear monoatomic chain

The interaction of waves in nonlinear media is of practical interest in the design of acoustic devices such as waveguides and filters. This investigation of the monoatomic mass–spring chain with a cubic nonlinearity demonstrates that the interaction of two waves results in different amplitude and frequency dependent dispersion branches for each wave, as opposed to a single amplitude-dependent branch when only a single wave is present. A theoretical development utilizing multiple time scales results in a set of evolution equations which are validated by numerical simulation. For the specific case where the wavenumber and frequency ratios are both close to 1:3 as in the long wavelength limit, the evolution equations suggest that small amplitude and frequency modulations may be present. Predictable dispersion behavior for weakly nonlinear materials provides additional latitude in tunable metamaterial design. The general results developed herein may be extended to three or more wave–wave interaction problems.

Experimental and Numerical Studies of Tethered DNA Shear Dynamics in the Flow-Gradient Plane

We use a combination of theoretical predictions and λ-phage DNA single molecule fluorescence microscopy to study the behavior of polymers tethered to surfaces. Brownian dynamics simulations of a number of coarse-grained polymer models—dynamic and equilibrium Kratky−Porod chains as well as bead−spring chains—were completed and compared with analytical and experimental results. Experiments of tethered λ-phage DNA in shear flow are presented for the first time in the flow-gradient plane. Cyclic dynamics—where the polymer continuously diffuses away from the wall, subsequently undergoes stretch in the flow direction, is then “entropically pulled back” toward the wall, and finally recoils—were observed and quantified through correlations and power spectral densities.

A Rubber-Reinforced Serial Chain of Torsion Springs for an Impulse Force Generator based on Snap-through Buckling of Closed Elastica

In this paper, we propose a rubber-reinforced serial chain of torsion springs for an impulse force generator based on snap-through buckling of closed elastica. The distinguished feature of the proposed device is to utilize an elastic energy of rubbers for generating impulse force. Utilizing an elastic energy of rubbers, its weight reduction of conventional ratio 11[%] is realized with maintaining its high elasticity and flexibility. The proposed device can generate the maximum momentum 14[Ns] with only the required maximum driving torque 15[Nm]. The values shows that the maximum momentum per unit of the maximum driving torque of the device is about 1.2 times as large as the impulse force generator using conventional one.

Experimental and Numerical Studies of Tethered DNA Shear Dynamics in the Flow-Gradient Plane

We use a combination of theoretical predictions and λ-phage DNA single molecule fluorescence microscopy to study the behavior of polymers tethered to surfaces. Brownian dynamics simulations of a number of coarse-grained polymer models—dynamic and equilibrium Kratky−Porod chains as well as bead−spring chains—were completed and compared with analytical and experimental results. Experiments of tethered λ-phage DNA in shear flow are presented for the first time in the flow-gradient plane. Cyclic dynamics—where the polymer continuously diffuses away from the wall, subsequently undergoes stretch in the flow direction, is then “entropically pulled back” toward the wall, and finally recoils—were observed and quantified through correlations and power spectral densities.

The role of spinodal region in the kinetics of lattice phase transitions

We consider a one-dimensional chain of phase-transforming springs with harmonic long-range interactions. The nearest-neighbor interactions are assumed to be trilinear, with a spinodal region separating two material phases. We derive the traveling wave solutions governing the motion of an isolated phase boundary through the chain and obtain the functional relation between the driving force and the velocity of a phase boundary which can be used as the closing kinetic relation for the classical continuum theory. We show that a sufficiently wide spinodal region substantially alters the phase boundary kinetics at low velocities and results in a richer solution structure, with phase boundaries emitting short-length lattice waves in both direction. Numerical simulations suggest that solutions of the Riemann problem for the discrete system converge to the obtained traveling waves near the phase boundary.