Rigid Cylindrical Surfaces Research Articles

Stability characteristics of Walter’s B viscoelastic fluid in a cylindrical configuration with heat transfer

The stability characteristics of the viscous fluid–viscoelastic fluid interface are investigated in a region confined by two rigid cylindrical surfaces. Walter’s B viscoelastic fluid is taken for the analysis and the fluid phases are transferring heat along with mass from one phase to the other. The gravitational acceleration effect is neglected and therefore, the interface is unstable due to surface tension. Using the linear stability analysis, the implicit expression for the critical wave number is derived analytically in terms of associated physical parameters and solved through the Newton–Raphson method. The various plots are made in terms of perturbations growth rate and critical wave number showing the behavior of flow variables. It is found that the instability of the interface decreases if the transfer of heat is increased. Walter’s B viscoelastic fluid interface is more unstable than the equivalent Newtonian fluid interface. The density of Walter’s B fluid resists the perturbation’s growth while viscoelasticity has an inverse effect.

On the mechanisms of production of large irreversible strains in materials with elastic, viscous and plastic properties

A thermodynamically and geometrically consistent mathematical model of large strains of materials with elastic, viscous and plastic properties is proposed. The viscous properties of a material are considered to provide a creep process and, therefore, the slow growth of irreversible strains during unloading and the stage preceding plastic flow. Under the fast growth of irreversible strains under the conditions of plastic flow, the viscous properties emerge as a mechanism that resists to this flow. Thus, the accumulation of irreversible strains initially occurs in the creep process, then under the plastic flow condition and finally because of material creep (during unloading). The change in the mechanism of irreversible strain growth occurs on elastoplastic boundaries moving in the deformed material. This change is only possible under the conditions of the continuity of irreversible strains and their rates. This continuity requires the coordination in the definitions of irreversible strain rates in the dependence on stresses, i.e. in laws of creep and plasticity. The change in the production mechanisms of irreversible strains means a different setting of the sources in differential equations of change (transfer equations) for these strains. Thus, irreversible strains are not divided into creep and plastic ones. The hypothesis of the independence of thermodynamic potentials (internal energy, free energy) from irreversible strains is applied with the aim of most visibility of the model relations. Under the condition of the acceptance of this hypothesis, an analogue of the Murnaghan formula is obtained, i.e. the stresses are completely determined by the level and distribution of the reversible strains as in the classical elastoplasticity theory. The main statements of the proposed model are illustrated by a boundary value problem solved in the framework of the model. This problem is about the deformation of an elastoviscoplastic material placed in the gap between two rigid cylindrical surfaces under the rotation of one of them and the material slipping in the neighbourhood of the internal surface.

Large irreversible deformations under conditions of changing mechanisms of their formation and the problem of definition of plastic potentials

The mathematical model of sequential growth of irreversible deformations in materials having elastic, viscous, and plastic properties is proposed. The model is illustrated by the solution of the problem on the occurrence of visco-plastic flow, its development, and deceleration in a material located between rigid cylindrical surfaces.

Measuring the accuracy of softball impact simulations

A study has been conducted to review viscoelastic and foam-constitutive models to describe sport ball response to impact with a rigid cylindrical surface. The impact model was developed to simulate a ball–bat collision. Comparisons were made to actual impacts, utilizing displacements recorded and analyzed using high-speed video capture. The resulting images and the ball geometry before impact were used as input to a computer-vision algorithm, which then produced a quantitative description of the deformation during impact. Foam-based material models were observed to match this observed deformation better (within 1 %) than viscoelastic material models (within 5 %). Both viscoelastic and foam material models deviated more from experimental data when describing dissipated energy and stiffness than when describing deformation. When describing impact energy dissipation and ball stiffness, the viscoelastic models deviated from experiment by more than a factor of two, while the foam material models exhibited up to 35 % error. The measured ball deformation, afforded through video analysis, has shown that foam material models are better able to describe ball impacts involving large energy dissipation, but require further refinement before equipment performance and design can be reliably performed.

Modeling of large elastoviscoplastic deformations with thermophysical effects taken into account

We propose a mathematical model of large elastoviscoplastic deformations where intensive deformation results in temperature increasing and heat transfer processes. As an example of applying the model relations, we present a solution of the boundary-value problem on rectilinear motion and heating of a medium located in the gap between coaxial rigid cylindrical surfaces.

The cellular response to curvature-induced stress

We present a theoretical model to explain recent observations of the orientational response of cells to unidirectional curvature. Experiments show that some cell types when plated on a rigid cylindrical surface tend to reorient their shape and stress fibers along the axis of the cylinder, while others align their stress fibers perpendicular to that axis. Our model focuses on the competition of the shear stress—that results from cell adhesion and active contractility—and the anisotropic bending stiffness of the stress fibers. We predict the cell orientation angle that results from the balance of these two forces in a mechanical equilibrium. The conditions under which the different experimental observations can be obtained are discussed in terms of the theory.

Accounting for the elastic properties of a non-Newtonian material under its viscosimetric flow

This paper considers the deformation and viscoplastic flow of a non-Newtonian material enclosed between coaxial rigid cylindrical surfaces, each of which performs a rotation followed by a stop and a rotation in the opposite direction. The problem is solved using the model of large elastoviscoplastic deformations, in contrast to the classical solutions obtained using the model of a rigid viscoplastic body. The parameters of the viscosimetric process are calculated in both the region of viscoplastic flow developed and the region of elastic deformation.

On the effects of different strategies in modelling balloon-expandable stenting by means of finite element method

In recent years, computational structural analyses have emerged as important tools to investigate the mechanical response of stent placement into arterial walls. Although most coronary stents are expanded by inflating a polymeric balloon, realistic computational balloon models have been introduced only recently. In the present study, the finite element method is applied to simulate three different approaches to evaluate stent-free expansion and stent expansion inside an artery. Three different stent expansion modelling techniques were analysed by: (i) imposing a uniform pressure on the stent internal surface, (ii) a rigid cylindrical surface expanded with displacement control and (iii) modelling a polymeric deformable balloon. The computational results showed differences in the free and confined-stent expansions due to different expansion techniques. The modelling technique of the balloon seems essential to estimate the level of injury caused on arterial walls during stent expansion.

Frictionless contact of two parallel congruent rigid cylindrical surfaces coated with thin elastic transversely isotropic incompressible layers: an analytic solution

Abstract The paper deals with a frictionless contact problem of two parallel rigid cylindrical surfaces, one encased in the other, coated with thin elastic transversely isotropic and incompressible layers. The coatings of the two circular cylinders may differ. A simplifying approximation for the displacement in the coating enables the problem to be formulated using stress and strain averaged through the coating thickness (for the method, see [Matthewson, M.J., 1981. Axi-symmetric contact on thin compliant coatings. J. Mech. Phys. Solids 29, 89–113]). Analytical results are obtained for the contact width and contact stress distribution. Given this contact stress distribution, an asymptotic analytical solution for the displacement in the coating is then obtained. The results are applied to the human ankle joint and generalized for articular cartilage with depth-dependent properties.

VIBRATIONS OF CIRCULAR PLATES RESTING ON A SLOSHING LIQUID: SOLUTION OF THE FULLY COUPLED PROBLEM

Vibrations of circular plates resting on a sloshing liquid free surface are studied. The fully coupled problem between sloshing modes of the free surface and bulging modes of the plate is solved by using the Rayleigh–Ritz method. The sloshing boundary condition is directly inserted into the eigenvalue problem. The liquid domain is limited by a rigid cylindrical surface and a rigid flat bottom. The fluid is considered inviscid and incompressible; it is described by the velocity potential expanded in a series. The present model has as limit cases: (1) circular plates resting on half-infinite liquid domain and (2) circular plates completely covering the liquid in a circular cylindrical tank. The theory is suitable for all axisymmetric plate boundary conditions. The effect of free surface waves on the plate natural frequencies is significant when the fundamental bulging mode of the plate has its natural frequency close to those of the first sloshing modes of the free surface. The present original solution allows the study of plates having a very strong coupling between sloshing and bulging modes to be studied to a high level of accuracy. The convergence of the method is shown. The natural frequencies and mode shapes for different system parameters are given.

A Transversely Isotropic Elastic Plate Pressed between Two Rigid Cylindrical Surfaces

This paper considers a fundamental contact problem of a transversely isotropic elastic plate pressed between two identical rigid cylindrical surfaces under concentrated loads. Two harmonic type stress functions are introduced under plane strain conditions and the method of Fourier transforms leads to a pair of dual integral equations which are reduced to Fredholm integral equations of the 2nd kind through the method of Abel transforms. The effects of anisotropy and plate thickness on the stresses and deformations as well as the contact pressure and the relations between load and contact area are examined.

Contact of Inflated Membranes With Rigid Surfaces

The equilibrium of an inflated cylindrical membrane in contact with two rigid cylindrical surfaces is considered. The cross section of the membrane consists of two circular arcs of radius R and an arc in contact with each surface. Equations for R and the end points of the contact regions are obtained. These equations are solved numerically for a membrane squeezed between parallel planes, and graphs of the results are shown. In addition we treat the case in which the cross section has ends which are attached to two points on one of the surfaces. In this case there are two solutions for certain values of the force on the planes, one of which is unstable.

Implementation of the Gas Squeeze-Film Foil Bearing

The squeeze-film gas bearing, a recent development in the technology of gas bearings, depends for its operation on the attainment of a relatively high-frequency low-amplitude repetitive normal displacement between the two solid surfaces that comprise a bearing. The frequency and amplitude requirements for this motion are usually such that the piezoelectric transducer constitutes an ideal driving source. The foil bearing, characterized by the low flexural rigidity of one of the mating bearing surfaces, is of particular interest in regard to such envisioned applications as guide bearings for magnetic tape, photographic film, and other foil materials, in high-performance computer-peripheral and electronic-optical recording apparatus. Experiments are described in which squeeze-film bearing action was achieved between various foil materials and a rigid cylindrical surface coupled to a tubular piezoelectric transducer driven in its circumferential mode of resonance. The results are discussed and reconciled to the theory of the squeeze-film gas bearing. Some criteria are established for design application of the foil squeeze-film bearing in this particular configuration.