Irreversible deformation and subsequent unloading of a spherical elastoviscoplastic layer

Analytical solutions of a number of one-dimensional quasi-static problems that describe the processes of elastic deformation of the material of a hollow sphere and of generation and development of the plastic flow in this material with increasing pressure on the external boundary are presented. The process of unloading during slow removal of the loading pressure is studied. Stress fields, fields of elastic and plastic strains in the material of the spherical layer, the law of motion of the elastoplastic boundary, and residual stresses are determined. It is demonstrated that (in contrast to the ideal plasticity case) the allowance for the viscous properties of the material during its plastic flow eliminates the possibility of plastic flow emergence during unloading.     

Photomechanical behavior of cellulose acetate under viscoelastoplastic deformation

To confirm the possibilities of cellulose acetate as a material for a model analysis during viscoelastoplastic deformation, the time-dependent photomechanical properties of the material were examined by means of creep tests under constant stress and recovery tests after removal of stress. Consequently, though the strain and the fringe order of cellulose acetate during creep and recovery are greatly influenced by stress and room temperature, both of them can be described simply by a power function of time, and the coefficient of each of these formulas can be represented by a function of the ratio of active stress to yield stress only. The effect of temperature is included in the formulation of the yield stress. In addition, the strain and the fringe order can be represented by the viscous-viscoelastic model proposed by Findleyet al.,^1,2 in which both of them are divided into four components: elastic, plastic, time-dependent irrecoverable viscous and time-dependent recoverable viscoelastic. The relation between viscoelastic strain and viscoelastic fringe order, and the relation between viscous strain and viscous fringe order were verified to be equivalent to that between plastic strain and plastic fringe order, all of which do not depend on stress, temperature or time. Therefore, the strain distribution of cellulose acetate under viscoelastoplastic deformation can be determined directly from the value of the fringe order measured.     

Study of the viscoelastoplastic deformation of an element of a body with a three-branch loading path

Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 12, pp. 26–33, December, 1991.     

Nonaxisymmetric deformation of open spherical shells with a curvilinear hole

A number of qualitative and quantitative mechanical effects are revealed in solving two-dimensional problems. Compression zones can occur in a thin shell with an oblong elliptical hole under internal pressure. The external edge has a strong effect on their position and size. In some cases, the fixed outer edge may stiffen the stress state near the hole __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 92–99, May 2008.     

A general hereditary multimechanism-based deformation model with application to the viscoelastoplastic response of titanium alloys

The formulation of a general model for the hereditary behavior of materials, in the viscoelastic and viscoplastic regimes, is presented. In this, we utilize the complete-potential structure as a general framework, together with the notion of strain- and stress- partitioning in terms of separate contributions of several submechanisms (viscoelastic and viscoplastic) to the thermodynamic functions (stored energy and dissipation). Detailed numerical treatments are given for both (i) the implicit integration algorithm for the governing flow and evolutionary rate equations of the model, and (ii) the automated parameter-estimation methodology (using the software code COMPARE) for characterization. For illustration, a specific form of the model presented is characterized for the TIMETAL 21S material using a very comprehensive test matrix, including creep, relaxation, constant strain-rate tension tests, etc. Discussion of these correlations tests, together with comparisons to several other experimental results, are given to assess the performance and predictive capabilities of the present model as well as the effectiveness and practical utility of the algorithms proposed.     

Ultimate deformation behavior of a laminated spherical shell

Summary A solution method is developed for a laminated spherical shell, subject to uniform normal tractions or constant radial displacements on the boundary. Displacements and stresses in the shell can be obtained from the solution formulas, which are as simple as those for homogeneous spherical shells. These formulas are accurate when the thicknesses of the constituent spherical layers are small in comparison with the radii of the shell, and become exact in case these thicknesses tend to zero under a fixed overall shell thickness. The solution is obtained mainly by exactly treating the product of an infinitely large number of matrices which link the displacements and stresses in different constituent spherical layers. A continuous analysis and a number of numerical results are provided to validate this development. Received 4 December 1996; accepted for publication 12 September 1997     

Motion through spherical droplet with non-homogenous porous layer in spherical container

The problem of the creeping flow through a spherical droplet with a nonhomogenous porous layer in a spherical container has been studied analytically. Darcy’s model for the flow inside the porous annular region and the Stokes equation for the flow inside the spherical cavity and container are used to analyze the flow. The drag force is exerted on the porous spherical particles enclosing a cavity, and the hydrodynamic permeability of the spherical droplet with a non-homogeneous porous layer is ca...     

NON-SYMMETRICAL LARGE DEFORMATION OF A SHALLOW THIN SPHERICAL SHELL

ＮＯＮ－ＳＹＭＭＥＴＲＩＣＡＬＬＡＲＧＥＤＥＦＯＲＭＡＴＩＯＮＯＦＡＳＨＡＬＬＯＷＴＨＩＮＳＰＨＥＲＩＣＡＬＳＨＥＬＬＷａｎｇＸｉｎｚｈｉ（王新志）ＲｅｎＤｏｎｇｙｕｎ（任冬云）ＷａｎｇＬｉｎｘｉａｎｇ（王林祥）ＹｅｈＫａｉｙｕａｎ（叶开沅）（Ｇａｎ...     

Tensile instability of nonlinear spherical membrane with large deformation

The problem on instability of nonlinear spherical membrane with large axisymmetric tensile deformations is investigated by using the bifurcation theory.It is proved that all singular points of the nonlinear boundary value problem must be simple limit points.The effect of loading and material parameters on the equilibrium state and its stability is discussed.     

Dynamics of a spherical particle in a laminar boundary layer

The problem of the motion of an individual spherical particle in a laminar boundary layer is considered for small Reynolds numbers determined from the relative velocity and the transverse velocity gradient of the flow undisturbed by the particle. The dependence of the transverse force acting on the particle, which results from the nonuniformity of the free stream, on the distance of the particle from the surface of a flat plate is calculated. It is shown that the direction of the transverse force changes with the distance of the particle from the plate: near the surface the force is positive, i.e., directed away from the plate, and at greater distances negative.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 91–96, November–December, 1990.The author wishes to thank M. N. Kogan and N. K. Makashev for useful discussions.     

Tangential oscillations of a differentially rotating spherical fluid layer

The natural harmonic oscillations of a differentially rotating fluid layer under the action of a potential force are considered. The rise in the layer level is assumed to be negligible. The oscillations satisfy an ordinary second-order differential equation with singular coefficients that depend on the spatial coordinate. This equation is solved by the method of local separation of singularities based on the use of the properties of the Fuchs series for a bounded solution. Various laws for the latitude dependence of the angular rate of ocean rotation and the effect of these laws on the problem spectrum are considered. An equation is obtained for the streamlines of the oscillations investigated. Two cases in which the latitude dependence of the base flow velocity coincides with the real dependence for a celestial body are considered and the corresponding modes are found.     

Instability of fluid motion in a thin spherical layer

We study flow stability in a thin spherical layer with respect to small disturbances. It is shown that for each given layer thickness there is a sequence of critical Reynolds numbers above which the motion is unstable. In its form, the critical disturbance is reminiscent of the secondary flow which develops upon loss of stability of the basic fluid flow between rotating cylinders (Taylor problem).The author wishes to thank M. I. Shliomis for his continued interest in this study.     

Dynamics of viscoelastoplastic soil under a moving wheel

A rate-dependent inelastic behavior or viscoelastoplastic behavior of soil subjected to dynamic loading of a moving rigid wheel is studied herein. A rational approach to this seemingly complex problem is treated in the context of continuum mechanics. Together with the concept of critical state soil mechanics for inelastic behavior we incorporate the so-called internal state variables for viscous effects. It is assumed that the free energy functional containing inelastic behavior may not be smooth for its entire domain of time histories. Rather, we assume a form of discretized free energy as a function of elastic strains, plastic strains, and internal or hidden variables of incremental quantity considered to be valid only for a small time interval or a fraction of loading increments. The finite element method is used to derive governing equations of motion. Exhaustive numerical examples are presented to demonstrate effectiveness of the present method.