Magnetorheology in viscoplastic media

Suspensions of iron particles in media with yield stresses were investigated to determine the effect of the continuous phase yield stress on the magnetorheological (MR) response. The steady-shear MR response was independent of the continuous phase yield stress for yield stresses in the range 0.9–37 Pa. The field-induced suspension yield stress increased sub-quadratically with the flux density. The small amplitude oscillatory shear response exhibited history dependence. The storage modulus depended not only on the magnitude of the applied magnetic field, but also on its history. This history dependence can be explained in terms of the field-dependent evolution of the suspension microstructure. Received: 24 February 1999 Accepted: 12 July 1999     

Rehodynamics of nonlinear viscoplastic media

It is known that the rheological behavior of many non-Newtonian media (including clay and cement suspensions) is best described by non-linear viscoplastic model.Exact results of the calculation of non-linear viscoplastic flows in circular, annular and plane transverse channels are given in terms of Saint-Venant numbers and non-linear parameters.     

Nonisothermal viscoplastic fluid flow through porous media

The Alishaev model [1] is extended to the case of nonisothermal flow. Neglecting conductive heat transfer, it is shown that for the model in question in the plane of the complex potential not only are the problems linear but the decoupling of the thermal and hydrodynamic problems is also allowed. The latter is reduced to a mixed problem for an analytic function. This makes it possible to use the wellknown methods and results of the theory of limiting equilibrium pillars for isothermal flow [2–5]. It is also established that the solutions of the unsteady problems tend asymptotically to the solutions of the corresponding steady-state problems and can be obtained from the latter by simpler conversion. The effectiveness of the approach proposed is illustrated with reference to the problem of a source-sink system [1–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 117–122, July–August, 1990.     

Cavitation bubble collapse in nonlinear viscous and viscoplastic media

The problem of the collapse of a bubble in nonlinear viscous and viscoplastic media under the influence of pressure at infinity is solved numerically. The pressure at which the radius of the bubble begins to decrease, the limiting radius of the bubble in the viscoplastic case and the critical collapse pressure where there is no plastic component are found. The critical pressure is found to be an order smaller than the corresponding value for a Newtonian viscous fluid. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 181–184, March–April, 1994.     

Cylindrical plane strain wave propagation in elastic/viscoplastic media

This paper discusses the influence of strain-hardening and of viscosity on the cylindrical elastic/viscoplastic wave-propagation. Perzyna's model is used with linear viscosity dependence, bilinear quasi-static stressstrain curve and a radial stress is assumed to be suddenly applied on the surface of a cylindrical cavity and maintained constant. It is shown by computer analysis that work-hardening and viscosity affect the results considerably and that at a certain time after the impact load is applied an elastic region appears within the viscoplastically deforming medium.     

Hydraulic impact of “exponential” and nonlinearly viscoplastic media in pipes made of a viscoplastic material

Differential equations are derived and the hydraulic impact process for “exponential” and nonlinearly viscoplastic media in pipes made of a viscoelastic material is analyzed. Hydraulic impact problems for actual media in pipes has been repeatedly treated in the literature [1–4]. The hydraulic impact of a viscous and linearly viscoplastic media in pipes made of an elastic and viscoelastic material was studied in this work. It is well known [5] that many media in the region of low and moderate shear rates reveal a nonlinearity of the flow curve (oil, drilling fluids, polymer solutions and melts, loaded fuels, fuel mixtures, blood, etc.). It should be noted that flexible pipes made of natural materials (pipe boreholes made of polymer materials, membranes of blood vessels, etc.) are described by complicated rheological equations of state for viscoelastic media. Thus a calculation of the influence of nonlinearity of these media and of the viscoelastic properties of the pipe material on the hydraulic impact process is of theoretical and practical interest in many engineering problems.     

A homogenization-based constitutive model for isotropic viscoplastic porous media

An approximate model based on the “second-order” nonlinear homogenization method is proposed to estimate the effective behavior of isotropic, viscoplastic, porous materials. The model is constructed in such a way that it reproduces exactly the behavior of a “composite-sphere assemblage” in the limit of hydrostatic loadings, and therefore coincides with the hydrostatic limit of Gurson’s criterion in the special case of ideal plasticity. As a consequence, the new model improves on earlier homogenization estimates, which have been found to be quite accurate for low triaxialities but overly stiff for sufficiently high triaxialities and nonlinearities. Additionally, the estimates delivered by the model exhibit a dependence on the third invariant of the macroscopic stress tensor, which has a nontrivial effect on the effective response of the material at moderate triaxialities. The proposed model is compared with exact results obtained for a special class of porous materials with sequentially laminated microstructures. The agreement is found to be quite good for the entire range of stress triaxialities, and all values of the porosity and nonlinearity considered.     

Laws of viscoplastic fluid flow in anisotropic porous and fractured media

In invariant tensor form, the laws of viscoplastic fluid flow are formulated for capillary and fractured media with a periodic microstructure that has orthotropic and transversely isotropic symmetry in the flow properties. An analysis of the laws of viscoplastic fluid flow in transversely isotropic and orthotropic porous and fractured media shows that in formulating the equations it is necessary to distinguish between the permeability tensor and the limiting gradient tensor, which may differ in the symmetry of the flow characteristics, and that the flow law is multivariant and admits one-, two-, and three-dimensional flows.     

Epstein transition zones in nonhomogeneous isotropic elastic media

A simple transformation in the independent variable makes it possible to obtain power series solutions of the stress equations of motion of elasticity for inhomogeneous elastic media whose refractive indices are represented by the Epstein profiles. Graphs of reflection and transmission coefficients versus angles of incidence are presented for different frequencies in the case of incident P as well as incident SV waves for some profiles.     

Calculation of limiting configuration of stagnant zones when viscoplastic oil is displaced by water

A study is made of the problem of determining the position of the limiting equilibrium portions of unrecovered viscoplastic oil displaced by water from a porous stratum in a many-well system. This problem was formulated by Bernadiner and Entov [1] and is of interest in connection with the obtaining of estimates of the volume of displaced oil. For two-dimensional isothermal flow in a homogeneous undeformed stratum and certain restrictions on the geometry of the flow region, the problem can be investigated by the methods of the theory of analytic functions [1–3]. An approximate solution of one problem with complicated flow geometry has been obtained [4] by means of potential theory. In the present paper the methods of the theory of jets are used to construct and analyze an exact analytic solution to the problem for three possible flow schemes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 77–81, March–April, 1991,We thank M. M. Alimov for discussing the work.     

Three-dimensional flows of thin layers of viscoplastic media in deformable channels and cavities

The problem of the three-dimensional flow of a viscoplastic medium in a thin layer bounded by two deformable material surfaces whose points are displaced transversely across the layer is formulated and solved. Expressions for the velocity components and the flow-rate and equations for calculating the pressure and the boundary of the shear flow region are obtained. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 201–205, July–August, 1998.     

A finite-strain model for anisotropic viscoplastic porous media: I – Theory

In this work, we propose an approximate homogenization-based constitutive model for estimating the effective response and associated microstructure evolution in viscoplastic (including ideally-plastic) porous media subjected to finite-strain loading conditions. The proposed model is based on the “second-order” nonlinear homogenization method, and is constructed in such a way as to reproduce exactly the behavior of a “composite-sphere assemblage” in the limit of hydrostatic loading and isotropic microstructure. However, the model is designed to hold for completely general three-dimensional loading conditions, leading to deformation-induced anisotropy, whose development in time is handled through evolution laws for the internal variables characterizing the instantaneous “ellipsoidal” state of the microstructure. In Part II of this study, results will be given for the instantaneous response and microstructure evolution in porous media for several representative loading conditions and microstructural configurations.     

Steady shearing in a viscoplastic solid

Steadyshearing solutions are found as quadratures within the context of a simple theory of viscoplasticity, which includes thermal softening and heat conduction. The solutions are illustrated by numerical examples for four commonly used versions of viscoplasticity, where each version has first been calibrated against the same hypothetical data set. It is found that, although they all predict qualitatively similar morphology, the four flow laws give results that differ in detail and one in particular differs substantially from the other three at the more extreme conditions. Although definitive data do not exist, there appears to be rough agreement with physical measurements of adiabatic shear bands. The conjecture is made that steady solutions correspond to central boundary layers for the full unsteady theory.     

Application of potential theory to a problem of the limiting configuration of the stagnant zones in the displacement of viscoplastic oil by water

A solution of the problem of determining the limiting-equilibrium portions of residual viscoplastic oil in connection with the displacement of oil by water from a porous formation in a multiwell system is constructed by the methods of potential theory and analyzed. The results of a comparison with a standard exact solution are presented for certain asymptotic cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 182–185, January–February, 1989.