Soft Cylinder Research Articles

Rolling friction—models and experiment. An undergraduate student project

In this paper the rolling friction (rolling resistance) model is studied theoretically and experimentally in undergraduate level fundamental general physics courses. Rolling motions of a cylinder along horizontal or inclined planes are studied by simple experiments, measuring deformations of the underlay or of the rolling body. The rolling of a hard cylinder on a soft underlay as well as of a soft cylinder on a hard underlay is studied. The experimental data are treated by the open source software Tracker, appropriate for use at the undergraduate level of physics. Interpretation of results is based on elementary considerations comprehensible to university students—beginners. It appears that the commonly accepted model of rolling resistance based on the idea of a warp (little bulge) on the underlay in front of the rolling body does not correspond with experimental results even for the soft underlay and hard rolling body. The alternative model of the rolling resistance is suggested in agreement with experiment and the corresponding concept of the rolling resistance coefficient is presented. In addition to the obtained results we can conclude that the project can be used as a task for students in practical exercises of fundamental general physics undergraduate courses. Projects of similar type effectively contribute to the development of the physical thinking of students.

A Proposed Simple Model for Estimating Occupational Radiation Dose to Staff from Veterinary 18F-FDG Pet Procedures

Several studies have been conducted concerning the radiation dose to hospital personnel from positron emission tomography (PET) radiopharmaceuticals, but to date only one parallel study has been conducted for veterinary staff. Veterinary patients present challenges not encountered with human patients, as they require anesthesia and therefore more intensive monitoring than human patients. This paper presents a simple model for estimating the effective radiation dose to veterinary staff using occupational dose data from PET studies at Colorado State University's (CSU) James L. Voss Veterinary Teaching Hospital. The model consists of three point sources within a soft tissue cylinder, and sample calculations are provided for estimating dose to nuclear medicine technologists and an anesthesia technologist based on four different sized dogs. The estimated doses are within the range of actual occupational doses published previously. There are different protocols for the sequence of events in veterinary PET, specifically the order of anesthesia induction and radiopharmaceutical injection. When F-FDG injection is performed prior to anesthesia induction, the estimated dose is between 1.5 and 3.6 times higher than the doses received if injection is done after anesthesia induction, although expected doses for both protocols are below occupational dose limits based on a case load of 100 veterinary patients per year. The model is based on the techniques used at CSU, but it can be modified for different hospitals as well as differently sized animals.

Micromagnetics of shape anisotropy based permanent magnets

In the search for rare-earth free permanent magnets, various ideas related to shape anisotropy are being pursued. In this work we assess the limits of shape contributions to the reversal stability using micromagnetic simulations. In a first series of tests we altered the aspect ratio of single phase prolate spheroids from 1 to 16. Starting with a sphere of radius 4.3 times the exchange length Lex we kept the total magnetic volume constant as the aspect ratio was modified. For a ferromagnet with zero magnetocrystalline anisotropy the maximum coercive field reached up to 0.5 times the magnetization Ms. Therefore, in materials with moderate uniaxial magnetocrystalline anisotropy, the addition of shape anisotropy could even double the coercive field. Interestingly due to non-uniform magnetization reversal there is no significant increase of the coercive field for an aspect ratio greater than 5. A similar limit of the maximum aspect ratio was observed in cylinders. The coercive field depends on the wire diameter. By decreasing the wire diameter from 8.7Lex to 2.2Lex the coercive field increased by 40%. In the cylinders nucleation of a reversed domain starts at the corners at the end. Smoothing the edges can improve the coercive field by about 10%.In further simulations we compacted soft magnetic cylinders into a bulk-like arrangement. Misalignment and magnetostatic interactions cause a spread of 0.1Ms in the switching fields of the rods. Comparing the volume averaged hysteresis loops computed for isolated rods and the hysteresis loop computed for interacting rods, we conclude that magnetostatic interactions reduce the coercive field by up to 20%.

BUCKLING AND SURFACE WRINKLING OF AN ELASTIC GRADED CYLINDER WITH ELASTIC MODULUS ARBITRARILY VARYING ALONG RADIAL DIRECTION

This paper investigates the buckling and surface wrinkling phenomena of an elastic graded cylinder under axial compression. We develop a semi-analytical finite element model based on elastic stability theory and the work of Lee et al. [Journal of Mechanics and Physics of Solids56 (2008) 858–868], which enables us to determine the critical compressive strain and corresponding wrinkling wavelength of a soft cylindrical structure with the shear modulus arbitrarily varying along the radial direction. A number of examples of practical interest have been explored to validate the proposed method, including: (i) surface wrinkling a soft cylinder with a hard outer surface, (ii) surface wrinkling of a soft cylindrical tube with a hard inner surface layer, (iii) buckling of a soft cylinder with an embedded hard layer, (iv) surface wrinkling of a soft cylinder covered by a bilayer, and (v) surface wrinkling of an elastic graded soft cylinder covered by a hard layer. The results demonstrate that the proposed method is valid for all these situations. In comparison to conventional finite element method, the discretization and meshing in the present method are much easier and the degrees of freedom involved are much smaller.

Torsion instability of soft solid cylinders

The application of pure torsion to a long and thin cylindrical rod is known to provoke a twisting instability, evolving from an initial kink to a knot. In the torsional parallel-plate rheometry of stubby cylinders, the geometrical constraints impose zero displacement of the axis of the cylinder, preventing the occurrence of such twisting instability. Under these experimental conditions, wrinkles occur on the cylinder's surface at a given critical angle of torsion. Here we investigate this subclass of elastic instability--which we call torsion instability--of soft cylinders subject to a combined finite axial stretch and torsion, by applying the theory of incremental elastic deformation superimposed on finite strains. We formulate the incremental boundary elastic problem in the Stroh differential form, and use the surface impedance method to build a robust numerical procedure for deriving the marginal stability curves. We present the results for a Mooney-Rivlin material and study the influence of the material parameters on the elastic bifurcation.

Spectral Analysis of Wave Propagation through Rows of Scatterers via Random Sampling and a Coherent Potential Approximation

A method is proposed for determining the modal spectra of waves supported by arrays, which are composed of multiple rows of scatterers randomly disordered around an underlying periodic configuration. The method is applied to the canonical problem of arrays of identical small acoustically soft circular cylinders and disorder in the location of the rows. Two different approaches are adopted to calculate the modes: (i) forming an ensemble average of the modes from individual realizations (loosely: extract information, then average); and (ii) extracting the modes from the ensemble average wave field (loosely: average, then extract information). Differences in the attenuation rates predicted by the two approaches, which cannot be attributed to numerical errors, are found for problems involving multiple wave directions and large disorder. A form of the coherent potential approximation (CPA) is also devised. Comparisons of the CPA to the results given by random sampling show that it gives high accuracy.

Waves in pre-stretched incompressible soft electroactive cylinders: exact solution

This paper studies wave propagation in a soft electroactive cylinder with an underlying finite deformation in the presence of an electric biasing field. Based on a recently proposed nonlinear framework for electroelasticity and the associated linear incremental theory, the basic equations governing the axisymmetric wave motion in the cylinder, which is subjected to homogeneous pre-stretches and pre-existing axial electric displacement, are presented when the electroactive material is isotropic and incompressible. Exact wave solution is then derived in terms of (modified) Bessel functions. For a prototype model of nonlinear electroactive material, illustrative numerical results are given. It is shown that the effect of pre-stretch and electric biasing field could be significant on the wave propagation characteristics.

Biomechanical modeling of surface wrinkling of soft tissues with growth-dependent mechanical properties

This paper explores growth induced morphological instabilities in biological soft materials. In view of that the growth of a living tissue not only changes its geometry but also can alter its mechanical properties, we suggest a refined volumetric growth model incorporating the effects of growth on the mechanical properties of materials. Analogy between this volumetric growth model and the conventional thermal stress model is addressed for both small and finite deformation problems, which brings great ease for the finite element analysis based on the suggested model. Examples of growth induced surface wrinkling behavior in soft composites, including core-shell soft cylinders and three-layered soft tissues, are explored. The results and discussions foresee possible applications of the model in understanding the correlation between the morphogenesis and growth of soft biological tissues (e.g. skins and tumors), as well as in evaluating the deformation and surface instability behavior of soft artificial materials induced by swelling/shrinkage.

Time-Dependent Fluid Squeeze-Out Between Soft Elastic Solids with Randomly Rough Surfaces

We study the time dependency of the interfacial separation and of the area of real contact between a soft elastic cylinder and a rigid solid with a randomly rough surface, squeezed with normal approach in a fluid. This problem is relevant for biological, as well as for bio-medical, seals and tires applications. An ad-hoc numerical scheme is developed to solve the transient mixed-EHD homogenized lubrication problem. We show that, for the soft contact case, the transition from the EHD to the boundary regime can be much more efficiently studied within a simplified (Grubin-like) problem formulation then with the full numerical scheme. This is not only of great conceptional importance, but also of practical importance as the latter calculation is much simpler and faster than the full scheme calculation.

Electrical Phenomena of Soft Particles. A Soft Step Function Model

Simple analytic expressions are derived for the electrophoretic mobility of a soft particle consisting of the hard particle core covered with an ion-penetrable surface layer of polyelectrolyte for the case where the electric potential is low. The effect of the distribution of the polymer segments is taken into account by modeling the surface layer as a soft step function with the inhomogeneous distribution width δ. It is shown that the electrophoretic mobility becomes lower than that for the hard step function model and that the maximum deviation of the soft step function model from the hard step function model, which is a function of λδ (where 1/λ is the softness parameter) and κ/λ (where κ is the Debye-Hückel parameter), is 2.7% at λδ = 0.1, 5.1% at λδ = 0.2, and 11% at λδ = 0.5. In the limit of very high electrolyte concentrations, the obtained mobility expression tends to the result derived from the conventional hard step function model. In addition, an analytic expression for the interaction energy between two similar soft plates is derived on the basis of the present soft step function model. The magnitude of the interaction energy is shown to decrease by a factor 1/(1 + κδ)(2). Approximate analytic expressions for the interaction energies between two similar soft spheres and between two similar soft cylinders are also derived with the help of Derjaguin's approximation.

Surface wrinkling and folding of core–shell soft cylinders

Constrained swelling or shrinkage of such soft materials as elastomers, polymeric hydrogels, and biological tissues can create various surface patterns through surface wrinkling and subsequent morphological evolution. Here we study, both theoretically and numerically, the swelling-driven surface wrinkling and pattern evolution of cylindrical elastomers with core–shell structure. The results demonstrate that the system may buckle into different morphologies under different geometric and material parameters. When the swelling of the shell or the shrinkage of the core reaches a threshold, the cylindrical surface will first buckle into a periodically buckling pattern. With further swelling/shrinkage, wrinkle-to-fold transition may occur, rendering a period-doubling surface topography. The energetic mechanisms underlying this process of wrinkling pattern evolution are analyzed. This study not only benefits the understanding of the morphogenesis in soft materials and tissues (e.g., tumors), but also opens a new avenue for the fabrication of multi-periodic or aperiodic patterns on curved surfaces through self-organization.

The direct and inverse problems of an air-saturated poroelastic cylinder submitted to acoustic radiation

A wave-fluid saturated poroelastic structure interaction model based on the modified Biot theory (MBT) and plane-wave decomposition using orthogonal cylindrical functions is developed. The model is employed to recover from real data acquired in an anechoic chamber, the poromechanical properties of a soft cellular melamine cylinder submitted to an audible acoustic radiation. The inverse problem of acoustic diffraction is solved by constructing the objective functional given by the total square of the difference between predictions from the MBT interaction model and diffracted field data from experiment. The faculty of retrieval of the intrinsic poromechanical parameters from the diffracted acoustic fields, indicate that a wave initially propagating in a light fluid (air) medium, is able to carry in the absence of mechanical excitation of the specimen, information on the macroscopic mechanical properties which depend on the microstructural and intrinsic properties of the solid phase.

Axial acoustic radiation force of progressive cylindrical diverging waves on a rigid and a soft cylinder immersed in an ideal compressible fluid

Background and motivation Previous works investigating the radiation force of diverging spherical progressive waves incident upon spherical particles have demonstrated the direction of reversal of the force when the particle is subjected to a curved wave-front. In this communication, the analysis is extended to the case of diverging cylindrical progressive waves incident upon a rigid or a soft cylinder in a non-viscous fluid with explicit calculations for the radiation force function (which is the radiation force per unit energy density and unit cross-sectional surface) not shown in [F.G. Mitri, Ultrasonics 50 (2010) 620–627]. Method A closed-form solution presented previously in [F.G. Mitri, Ultrasonics 50 (2010) 620–627] is used to plot the radiation force function with particular emphasis on the difference from the results of incident plane progressive waves versus the size parameter ka ( k is the wave number and a is the cylinder’s radius) and the distance of the cylinder from the acoustic source r 0. Results Radiation force function calculations for the rigid cylinder unexpectedly reveal that under specific conditions determined by the frequency of the acoustic field, the radius of the cylinder, as well as the distance to the acoustic source, the force becomes attractive (negative force). In addition, the numerical results show that the radiation force on a rigid cylinder does not generally obey the inverse-distance law with respect to the distance from the source. Conclusion and potential applications These results suggest that it may be possible, under specific conditions, to pull a cylindrical structure back toward the acoustic source using progressive cylindrical diverging waves. They may also provide a means to predict the radiation force required to manipulate non-destructively a single cylindrical structure. Potential applications include the design of a new generation of acoustic tweezers operating using a single beam of progressive waves (in contrast to the traditional version of acoustical tweezers in which an acoustic standing wave field is produced using two counter-propagating acoustic fields) for investigations in the field of flow cytometry, particle manipulation and entrapment.

540 水を充填した柔軟円筒による車体弾性振動の減衰効果(自動車・鉄道車両の制震,OS-3 ダンピング,総合テーマ「伝統を,未来へ!」)

540 水を充填した柔軟円筒による車体弾性振動の減衰効果(自動車・鉄道車両の制震,OS-3 ダンピング,総合テーマ「伝統を,未来へ!」)

Anti-plane shear fracture of the interface in a cylindrical smart structure with functionally graded magnetoelectroelastic properties

The purpose of the present work is to study the fracture behavior of the arc-shaped interface in a cylindrical non-homogeneous magnetoelectroelastic structure. Fracture analysis is performed by the method of Cauchy singular integral equation. Parametric studies are conducted on the stress intensity factor, and practical guidelines are given for the optimization of fracture performance. (a) The ratio between the outer and inner radii should be at least 1.1. (b) A softer inner side plus a stiffer outer side is a good non-homogeneity design for the magnetoelectroelastic layer. (c) A soft central cylinder and a stiff outer magnetoelectroelastic layer constitute a good stiffness matching on the interface.

Surface patterning of soft polymer film-coated cylinders via an electric field

Using the linear stability analysis method, we investigate the surface wrinkling of a thinpolymer coating on a cylinder in an externally applied electric field. It is demonstrated thatenergy competition between surface energy, van der Waals interactive potential energy andelectrostatic interaction energy may lead to ordered patterns on the film surface. Theanalytical solutions are derived for the critical conditions of both longitudinal andcircumferential instabilities. The wavelengths of the generated surface patternscan be mediated by changing the magnitude of the electric field. Our analysisshows that the surface morphology is sensitive to the curvature radius of the fiber,especially in the micrometer and nanometer length scales. Furthermore, we suggesta potential approach for fabricating hierarchical patterns on curved surfaces.

Structure-Tunable Bidirectional Hybrid Nanowires via Multicompartment Cylinders

We present structure-tunable bidirectional inorganic-organic hybrid nanowires templated by soft multicompartment cylinders, possessing perfectly parallel compartments. The poly(2-vinylpyridine) compartments are used to bind nanoparticles via supramolecular coordination. The resulting hybrid nanowires are tunable in terms of the distribution of the inorganics in the corona. The two limiting cases are (a) perfectly aligned, parallel nanowires and (b) nanowires with one homogeneous corona. This approach demonstrates how advances in polymer architectures can be used to create novel hybrid materials of unprecedented complexity and very desirable architecture.

Electrostatic interaction between two cylindrical soft particles

An expression for the potential energy of electrostatic interaction between two soft cylinders (i.e., polyelectrolyte-coated cylindrical particles) in an electrolyte solution is derived by applying Derjaguin's approximation to the corresponding interaction energy between two parallel soft plates for the case where the density of fixed charges within the polyelectrolyte layer is low. The interaction between two parallel cylinders and that between two crossed cylinders are considered. The obtained expression covers various limiting cases that include hard cylinder/hard cylinder interaction, cylindrical polyelectrolyte/cylindrical polyelectrolyte interaction, soft cylinder/cylindrical polyelectrolyte interaction, soft cylinder/hard cylinder interaction, and cylindrical polyelectrolyte/hard cylinder interaction.

Scattering by acoustic boundary scatterers with small wave sizes and their reconstruction

The scattering efficiencies of hard and soft cylindrical scatterers are compared using the Novikov-Grinevich-Manakov functional algorithm designed to reconstruct two-dimensional scatterers. The existence of a rigid relationship between the amplitude and phase of the wave scattered by a quasi- point-like scatterer and by scatterers with small wave sizes in the form of a soft cylinder, a soft sphere, and an air bubble in a liquid is confirmed by numerical simulations.

Three-dimensional transient and harmonic shear-wave scattering by a soft cylinder for dynamic vascular elastography

With the objective of characterizing biological soft tissues with dynamic elastography, a three-dimensional (3D) analytical model is proposed to simulate the scattering of plane shear waves by a soft cylinder embedded in an infinite soft medium. The 3D problem of harmonic plane shear-wave scattering is first formulated and solved, and the monochromatic solution is employed to simulate transient wave scattering. Both harmonic and transient simulations are compared with experimental 3D acquisitions. The good agreements obtained between measured and calculated displacement fields allowed to conclude on the validity of the proposed 3D harmonic and transient models. The spatial distribution of displacements (diffraction lobes, displacement oscillations, wave diffraction angles, etc.) and their relative amplitudes in both inclusion and surrounding materials depended on the contrast between the viscoelastic properties of the different media. The possibility of solving an inverse problem to assess soft heterogeneous medium viscoelasticity is discussed and some future theoretical and experimental developments are proposed.