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A solution is obtained for the coupled boundary value problem of non-isothermal deformation of a material forming a finite-length plug in a non-deformable round pipe. Under conditions of rigid adhesion to the pipe surface, the material is deformed under the action of a variable pressure drop specified on the end surfaces of the plug. Irreversible deformation is associated with both creep and viscoplastic flow of the material and causes its heating. Additionally, the dependences of the yield strength, viscosity coefficient, and creep parameters of the material on temperature are taken into account. Using the large deformation model, the processes of creep and viscoplastic flow with increasing and constant pressure drop, flow braking and unloading of the medium with decreasing pressure, as well as cooling of the material after complete removal of the mechanical load are studied. [ABSTRACT FROM AUTHOR]

The results of calculations of the stress-strain states of an elastoplastic material containing a single cylindrical continuity defect and loaded with external pressure are presented. The hydrostatic pressure on the surface distant from the defect initially increases, remains constant for some time and then gradually decreases to zero. The process of comprehensive compression leaves, after unloading, a formed level and distribution of residual stresses in the vicinity of the continuity defect. The change in such stresses is calculated upon repeated loading and unloading. Intensity and nature of repeated loads are considered identical to the original ones. Calculations are carried out within the framework of the stated one-dimensional problem of the theory of large deformations. The material is assumed to be incompressible. The development of areas of viscoplastic flow in the active part of the process and their attenuation during unloading are taken into account. Changes in the geometric dimensions of the evolving defect are assessed. [ABSTRACT FROM AUTHOR]

With the use of a mathematical model of large deformations of materials with elastic, plastic, and viscous properties, an analytical solution was obtained for deformation under creep conditions of a plug in a round tube with a varying pressure drop. The motion is considered taking into account the sliding of the material in the vicinity of the rigid wall of the pipe and its deformation under increasing, constant, and decreasing pressure. The displacements, reversible and irreversible deformations, and stresses at all stages of deformation, including residual deformations and stresses at full unloading, are calculated. [ABSTRACT FROM AUTHOR]

We present the solution of a coupled problem on large deformations in a heavy layer of a material with elastic, viscous and plastic properties. The layer is held by a rigid inclined plane and is subjected to thermomechanical effects on its free surface. The contact of the layer material with the holding inclined plane is assumed to be rigid. Its other boundary plane is loaded and heated. Reversible and irreversible strains in the layer material are specified by differential equations of their change. Parameters of adopted constitutive laws of creep and plastic flow are considered to be temperature dependent. Strains, stresses and temperature are calculated at each time point of the deformation process. The conditions for the onset and termination of viscoplastic flow are indicated. The patterns of the motion of elastoplastic boundaries are established both during the active process of heating and loading, and during cooling and unloading. [ABSTRACT FROM AUTHOR]

A method is proposed and the results of calculations are discussed in the coupled problem of the theory of large deformations on the deformation of the material of a cylindrical layer between rigid cylindrical surfaces. The layer material is assumed to be elastoviscoplastic, and its contact with the rough boundaries when the outer one is rotated is accompanied by friction, which generates heat; irreversible deformation is also considered to be calorific. The total cycle of the process of quasi-static deformation is calculated from its beginning to complete unloading and cooling of the material layer. The time points of the beginning and end of the sliding of the material along its rigid boundary surface and the beginning and end of its near-wall viscoplastic flow are indicated. [ABSTRACT FROM AUTHOR]

Calculations are given of the distribution of strains, stresses, and temperature during the deformation of an elastoviscoplastic material clamped between coaxial cylindrical surfaces and initially retained by dry friction against the boundary surfaces. Due to the given variable advancement of the outer of them, the material slips and its viscoplastic flow begins (not simultaneously). The process of flow development with its subsequent deceleration to a stop, material unloading and cooling to room temperature is considered. Heat is produced by sliding friction against a rough boundary surface and by irreversible deformation (a related problem of large deformation theory). A deformable material is considered to be mechanically incompressible, when the change in its volume is associated only with thermal expansion, the yield strength is assumed to depend on temperature. [ABSTRACT FROM AUTHOR]

A solution for a coupled thermomechanical boundary value problem of the theory of large deformations that simultaneously takes into account the intense deformation of an elastoviscoplastic material and its heating due to such deformation and near-wall friction is constructed. The conditions for the emergence and development of a viscoplastic flow in the material of a cylindrical layer enclosed between rigid surfaces, one of which has the ability to rotate under the action of a changing given load relative to the axis of the viscometer, are calculated. At all stages of the process from its start to stop, the stress-strain state and temperature distributions in the areas of flow and reversible deformation are calculated, including flow stop, unloading and cooling, with the calculation of residual stresses and deformations. The yield strength is assumed to be temperature dependent. [ABSTRACT FROM AUTHOR]

The problem of deformation of an elastic-viscoplastic material in the gap between the coaxial cylindrical surfaces of a rotary viscometer is considered. The loading of the material occurs due to a slow rotation of the outer wall of the viscometer; at this stage, the condition of adhesion of the material to the walls is assumed. At a certain critical angle of rotation, material slip occurs, which causes the unloading shock wave to propagate in the layer. When the wave propagates, it interacts with the elastic-plastic boundary and is reflected from the walls of the viscometer. The unloading dynamics is investigated using the ray method for constructing near-front expansions. [ABSTRACT FROM AUTHOR]

A mathematical model of large deformations is used to solve a coupled boundary-value problem about the deformation of an elastoviscoplastic material in a cylindrical viscometer with account for its heating due to wall friction. The deformation of a material enclosed between rigid surfaces due to the rotation of an inner cylindrical surface at a variable velocity is investigated. It is taken into account that a yield point depends on temperature. The motion of elastoplastic boundaries is described. Stresses, strains, and temperature in a thermoelastic deformation region and in a flow region both during the development of the flow and during its deceleration, including stopping, unloading, and cooling, are calculated. Residual stresses and deformations are determined. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the solution of a coupled problem on creep and viscoplastic flow in a flat heavy layer. The layer is on an inclined surface and subject to heating and cooling. The problem has been solved in the framework of the large elastoplastic strain mathematical model, which generalized for the case of taking into account rheological and thermophysical material properties. The thermophysical and deformation processes are interconnected; a yield limit, a viscosity factor and creep parameters depend on temperature. The patterns of the motion of elastoplastic boundaries are shown, stresses, strains and strain rates in the areas of flow and thermoviscoelastic deformation has been calculated. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of deformation of a disk rotating with changing angular velocity under consecutive accumulation of creep and plastic strains. The differential equations which help to calculate the fields of stresses, strains, displacements and velocities are obtained; the method of finite difference is used for solving the problem. The evolution of the viscoplastic flow region is investigated. The Norton power law is used as creep law; the von Mises's generalized yield criterion is applied as viscoplastic flow condition. The obtained solution is compared to the classical elastoplasticity case. A hollow disk and a disk with a rigid inclusion are studied. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The theory of large deformations is used to solve the problem of deformation of an elastoviscoplastic material placed in a gap between two coaxial cylindrical surfaces, with one of them rotating with an alternating rate and the other one at rest. It is shown that an increase in the stresses in a cylindrical layer due to a mechanical influence on it initially causes irreversible creep strains because of viscosity of the material and then the accumulation of plastic strains because of the arrival of stress states at the loading surface. The unloading is accompanied by a plastic strain and then a viscous one. The stress-strain parameters of the medium with a varying rotation rate of the cylinder are calculated. Stress relaxation after the complete stop of a cylinder is described. [ABSTRACT FROM AUTHOR]

Abstract: It is proposed to divide the process of accumulation of irreversible deformations by a deformable solid into successive parts differing in the mechanisms of production of such deformations. With the growth of stresses in the solid due to mechanical action on it, initially irreversible deformations are produced due to the viscous properties of the material of the deformed solid as a creep deformation, and, when the stressed states emerge onto the loading surface, the mechanism of their production changes to plastic. Under unloading, the sequence reverses from a rapid plastic to a slow viscous mechanism. The continuity in such a growth of irreversible deformations is provided by the corresponding set of creep and plasticity potentials. The features of this approach are illustrated by the solution of the boundary-value problem of elastoplastic deformation on the compression of the spherical layer by an external uniform pressure, when the viscous properties of the material are specified using the Norton creep power law and the properties of the ideal plastic—by the plastic potential in the form of the Mises plasticity condition. [ABSTRACT FROM AUTHOR]

The one-dimensional dynamic problem of the theory of large elastic-plastic deformations is considered for the interaction of an unloading wave with an elastic-plastic boundary. It is shown that before the occurrence of the unloading wave, the increasing pressure gradient leads to quasistatic deformation of the elasti©viscoplastic material filling the round tube, which is retained in the tube due to friction on its wall, resulting in the formation of near-wall viscoplastic flow and an elastic core. The unloading wave is initiated at the moment of the onset of slippage of the material along the inner wall of the tube. Calculations were conducted using the ray method of constructing approximate solutions behind strong discontinuity surfaces, and ray expansions of the solutions behind the cylindrical surfaces of discontinuities were obtained. [ABSTRACT FROM AUTHOR]

Within the framework of the model of large deformations, the deformation of a material exhibiting elastic, viscous, and plastic properties and placed between two rigid cylinders is investigated when turning the internal cylinder. The accumulation of irreversible deformations prior to the onset of plastic flow and upon its termination is associated with creep. Reversible and irreversible deformations according to the model in question are determined by differential transport equations. To calculate the displacement fields, stresses, and reversible, irreversible, and complete deformations, a system of partial differential equations is obtained, for which a finite-difference scheme is constructed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The problem of deformation of a horizontal plane layer of a compressible material is solved in the framework of the theory of small strains. The upper boundary of the layer is under the action of shear and compressing loads, and the no-slip condition is satisfied on the lower boundary of the layer. The loads increase in absolute value with time, then become constant, and then decrease to zero. Various plasticity conditions are consideredwith regard to the material compressibility, namely, the Coulomb-Mohr plasticity condition, the von Mises-Schleicher plasticity condition, and the same conditions with the viscous properties of the material taken into account. To solve the system of partial differential equations for the components of irreversible strains, a finite-difference scheme is developed for a spatial domain increasing with time. The laws of motion of elastoplastic boundaries are presented, the stresses, strains, rates of strain, and displacements are calculated, and the residual stresses and strains are found. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The one-dimensional deformation of a material and subsequent unloading in the vicinity of a single cylindrical discontinuity is calculated using the theory of large viscoelastoplastic strains. Emphasis is on the formation of a residual stress field during the loading-unloading process and the effect of the viscous properties of the material on the level and distribution of these stresses. A comparison is performed with results of solution of the corresponding problem using the theory of large elastoplastic strains. [ABSTRACT FROM AUTHOR]

The article reports on analytical solutions for the case of viscoplastic flows of a Shvedov Bingham material, taking into consideration the elastic properties of the material. The material is treated as incompressible, and its viscosity is manifested only in the course of the plastic flow. Both the stress and strain distributions, as well as the initial moment, are determined by the properties of the material. Applying boundary conditions at equilibrium, the solution to the problem is found out mathematically.

Examines the deformation of a thick-wall pipe under pressure applied to its external cylindrical surface. Model of elastoplastic strains; Plastic flow during unloading; Transport equations.