Rigid Coaxial Cylindrical Surfaces Research Articles

On the Changing Mechanisms of the Production of Large Irreversible Deformations in the Conditions of Rectilinear Motion in a Cylindrical Layer

In the framework of the theory of large deformations, a solution is obtained for the deformation of a material with nonlinear elastic, plastic and viscous properties located in the gap between two rigid coaxial cylindrical surfaces. The outer surface remains stationary, and the inner rectilinearly moves with variable speed. With uniformly accelerated surface motion, initially irreversible strains accumulate due to the viscous properties of the material as creep strains, and when the stressed state exits to the loading surface, the appearance and development of the viscoplastic flow region are considered. The further development of the flow at a constant speed and its deceleration at equally slow motion of the surface to a complete stop were investigated. The parameters of the stress-strain state of the medium are calculated, and stress relaxation after a complete stop of the cylinder is investigated.

Torsion with Circular Shear of a Mooney–Rivlin Solid

The axisymmetric torsion of a layer of incompressible Mooney–Rivlin material placed between two rigid coaxial cylindrical surfaces is considered. It is assumed that the ends of the cylinder are fixed to avoid axial displacement and the cross-sections orthogonal to the axis of symmetry do not distort during deformation. In this case, the material points move along arcs of circles with an angular velocity which in the general case may depend on both the axial and the radial coordinates. Closed-form solution of the equilibrium equation is obtained. The well-known Rivlin solution is a particular case of this solution. Like in the classical solution, the stress tensor is a function of only the radial coordinate and the twist angle of the material points is a linear function of the axial coordinate. It is shown that torsion that is symmetric about a plane orthogonal to the axis of rotation can be realized only within the framework of the Rivlin solution. The obtained exact solution can be realized in the presence of friction on cylindrical surfaces. The initial-boundary-value problem described by this solution is considered.

Mathematical modeling of creep and viscoplastic flow of a cylindrical layer material

Within the framework of a mathematical model of large elastoplastic deformations, taking into account viscous properties of materials, a boundary value problem of creep and viscoplastic flow of a material in the gap between two rigid coaxial cylindrical surfaces under rectilinear motion of the inner surface is considered. Irreversible deformations accumulate from the beginning of the deformation process and are initially associated with the creep process of the material, which is described using the Norton creep power law. With a subsequent increase in the speed of movement of the inner cylinder at some time point, the stress state will reach the yield surface and a viscoplastic flow will begin in the material. As a plastic potential, we use the Tresca yield criterion, generalized in the case of taking into account the viscous properties of the material. The viscoelastic deformation, the emergence and development of the viscoplastic flow under uniformly accelerated motion of the inner surface, the flow under constant speed, and the flow inhibition under equal slow motion of the surface to a full stop are considered. Stresses, reversible and irreversible deformations, displacements are calculated, stress relaxation after the complete stop of the cylinder is investigated.

On Finite Displacement of an Elastoviscoplastic Material in a Gap between Two Rigid Coaxial Cylindrical Surfaces

In the framework of the theory of large deformations, we obtain the solution of a boundary value problem on the flow of an elastoviscoplastic material in a gap between two rigid coaxial cylindrical surfaces under pressure drop changing with time. It is assumed that slip of the material is possible on both surfaces. We consider reversible deformation, the development of viscoplastic flow under the increasing and constant pressure drop, deceleration of the flow under the decreasing pressure drop, and the unloading of the medium.

Deformation and Heating of an Elastoviscoplastic Cylindrical Layer Moving Owing to a Varying Pressure Drop

Within the framework of the theory of large elastoplastic deformations generalized to the case of viscous and thermophysical properties of materials, we give a solution of a sequence of coupled problems on the onset and development of a flow in a material layer filling the gap between two rigid coaxial cylindrical surfaces under increasing pressure drop and on the subsequent flow deceleration under decreasing pressure gradient. Here the thermophysical and deformation processes are coupled, and the yield stress depends on temperature. Heat production due to the layer material friction against the rough cylindrical boundary surfaces is taken for an additional heat source.

Helical Viscoplastic Flow in a Gap between Rigid Cylinders

In this paper, the problem of viscoplastic flow of an incompressible non-Newtonian material between two rigid coaxial cylindrical surfaces in the case of helical motion of each of the cylinders is solved. The deformation under an increasing, constant, and decreasing loading is considered. The problem is solved by using the model of large elastoviscoplastic strains. The parameters of the processes under study are calculated for the domains of reversible strain, for the domains of viscoplastic flow, and for the unloading domains.

Creep and stress relaxation in the material of a cylindrical layer in its linear motion

Within the framework of the theory of large deformations, we consider deformation of some material with nonlinear elastic and viscous properties that is located in the gap between two rigid coaxial cylindrical surfaces when the inner surface moves rectilinearly. We study the uniformly acceleratedmotion of the inner cylinder, its subsequentmotion with a constant speed, and further deceleration till the full stop. We calculate stresses, reversible and irreversible deformations, displacements and study the stress relaxation after the full stop of the cylinder.

Straight flow in an elastoviscoplastic cylindrical layer with possible two-sided slip

The solution of the boundary value problem of the theory of large strains dealing with the viscoplastic flow of an elastoviscoplasticmaterial in the gap between two rigid coaxial cylindrical surfaces in the case of motion of the inner surface is obtained under the assumption that the material can slip on both surfaces. The reversible deformation, the development of a viscoplastic flow in the cases of uniformly accelerated and constant-velocity motions of the surface, the flow deceleration in the case of uniformly decelerated motion of the surface until full stop, and the unloading of the medium are considered.

Flow of an elastoviscoplastic material between rotating cylindrical surfaces with nonrigid cohesion

The theory of large deformations is used to construct exact solutions of a sequence of one-dimensional boundary-value problems of the occurrence, development, and subsequent deceleration of viscometric flow of an elastoviscoplastic incompressible material located in the gap between rotating rigid coaxial cylindrical surfaces. In the quasistatic approximation allowing for slip of the material on its solid boundaries, the flow initiation conditions in the deformed material and the laws of motion of the boundary surfaces of the flow of this material both during its development and deceleration are determined. The parameters of the stress-strain states in the regions of reversible deformation and flow in all stages of the process, including the cessation of the flow and the complete unloading by rotation of the solid boundary in the opposite direction, are calculated.

Viscosimetric flow of an incompressible elastoviscoplastic material under the presence of a lubricant on the boundary surfaces

Generalizing the model of large deformations by accounting for the viscous properties of materials, we obtain the analytical solutions of some quasistatic boundary value problems concerning the viscosimetric flows of an elastoviscoplastic material in the gap between the rigid coaxial cylindrical surfaces when, in the neighborhood of one of the rigid cylinders (either internal or external), there is a layer of an elastic non-Newtonian lubricant, and the rigid adhesion conditions are satisfied on boundary surfaces. The conditions are studied of origination of a flow in the lubricant layer and in the basic material. The values of the maximum velocity are specified under which the flow does not tresspass the lubricant layer.

Development of a rectilinear axisymmetric viscoplastic flow and elastic aftereffect after its stop

An analytical solution is given for the boundary-value problem of the theory of large elastoviscoplastic strains for rectilinear motion of a material in the gap between two rigid coaxial cylindrical surfaces. The cases of initially uniformly accelerated motion with the subsequent uniformly decelerated stop of one of the surfaces when the other surface remains motionless are considered. The laws of motion of the elastoplastic boundaries and distributions of displacements and stresses, including residual ones, are given.

The pressing of an elastoviscoplastic material between rigid coaxial cylindrical surfaces

An analytical solution of the problem of the pressing of an incompressible elastoviscoplastic material between two rigid coaxial cylindrical surfaces is obtained using the theory of large strains. The velocity of motion of the elastic core, the change in the dimensions of the zones of irreversible deformation and the stresses and strains both in the elastic core and in the flow region are calculated as a function of the variable pressing force.

Variations in the Earth's gravity field caused by torsional oscillations in the core

SUMMARY We investigate whether a component of the flow in the Earth's fluid core, namely torsional oscillations, could be detected in gravity field data at the surface and whether it could explain some of the observed time variations in the elliptical part of the gravity field (J2). Torsional oscillations are azimuthal oscillations of rigid coaxial cylindrical surfaces and have typical periods of decades. This type of fluid motion supports geostrophic pressure gradients, which produce deformations of the core–mantle boundary. Because of the density discontinuity between the core and the mantle, such deformations produce changes in the gravity field that, because of the flow geometry, are both axisymmetric and symmetric about the equator. Torsional oscillations are thus expected to produce time variations in the zonal harmonics of even degree in the gravity field. Similarly, the changes in the rotation rates of the mantle and inner core that occur to balance the change in angular momentum carried by the torsional oscillations also produce zonal variations in gravity. We have built a model to calculate the changes in the gravity field and in the rotation rates of the mantle and inner core produced by torsional oscillations. We show that the changes in the rotation rate of the inner core produce changes in J2 that are a few orders of magnitude too small to be observed. The amplitudes of the changes in J2 from torsional oscillations are 10 times smaller than the temporal changes that are observed to occur about a linear secular trend. However, provided the mechanism responsible for these changes in J2 is identified and that this contribution is removed from the data, it may be possible in the future to detect the lowest harmonic degrees of the torsional oscillations in the gravity field data. We also show that torsional oscillations have contributed to the linear secular change in J2 by about −0.75 × 10−12 per year in the last 20 years. Finally, the associated change in the vertical ground motion at the surface of the Earth that is predicted by our mechanism is of the order of 0.2 mm, which is too small to be detected with the current precision in measurements.