Method of determining the volume and shear characteristics of elastico-viscous hereditary media from uniaxial-tension (compression) experiments

A method is proposed for determining the elastic constants — instantaneous modulus of elasticity, Poisson's ratio, shear modulus, bulk modulus, and the shear and volume influence functions — the shear creep kernel, the shear creep rate kernel, and the corresponding relaxation kernels from the data of creep or relaxation tests.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 754–758, July–August, 1969.     

Solution of the problem of the plane deformation of a tube made of physically nonlinear quadratic viscoelastic material

An exact solution is obtained for the problem of the plane deformation of a tube of quadratically nonlinear viscoelastic material characterized by four kernels. For given boundary pressures the solution contains functions determined from simple creep and relaxation tests for stresses and strains lying in the region of linearity of the relation. In accordance with the method of approximations for nonlinear materials [9], an approximation is given for a series of convolution integrals of increasing multiplicity in transforms and inverse transforms together with an error estimate.Moscow Institute of Electronic Engineering. Translated from Mekhanika Polimerov, No. 1, pp. 117–123, January–February, 1973.     

Method of approximations for solving problems of the linear theory of thermoviscoelasticity

A general approximate method of solving problems of the linear theory of thermoviscoelasticity is proposed. Use is made of the Laplace transformation and certain properties of the dependence of solutions to problems of the theory of elasticity on Poisson's ratio that make possible a simple approximation. As a result, the inverse transforms become elementary and the general solution of the problem is expressed by creep and relaxation functions.Mekhanika Polimerov, Vol. 4, No. 2, pp. 210–221, 1968     

Viscoelastic characteristics of the interaction between structures and soils

The shear coefficients of a body relative to the soil and the shear creep and relaxation kernels are determined from the data of creep and relaxation tests.Urazbaev Institute of Mechanics and Earthquake Resistance of Structures, Academy of Sciences of the SSR, Tashkent. Translated from Mekhanika Polimerov, No. 2, pp. 207–211, March–April, 1973.     

An axisymmetric problem of viscoelasticity

The problem of a long hollow viscoelastic cylinder, enclosed in an elastic shell and loaded by internal pressure, is considered. Two cases are investigated: 1) the shear and volume relaxation kernels are proportional; 2) the shear and volume creep kernels are proportional. Resolving integral equations with singular kernels of a nondifference type are obtained and a method of solution is proposed. The convergence of the method is proved.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 5, pp. 798–805, September–October, 1969.     

Quasilinear theory of viscoelasticity

By postulating equal contributions the number of kernels in the principal cubic theory of viscoelasticity and in the theory with regular kernels of two arguments is reduced to three. For certain quasilinear relations all the kernels and functions are determined from creep, relaxation, and simple loading and deformation tests. In the case of simple loading and deformation the problems for a viscoelastic incompressible material reduce to problems of the theory of small elastoplastic deformations of an incompressible material. Several problems relating to this case are considered.Moscow M. V. Lomonosov State University. Translated from Mekhanika Polimerov, No. 4, pp. 603–611, July–August, 1969.     

Creep on an initial small interval

The creep processes of hereditary media on a small initial interval are described, using as influence functions the resolvent functions for the generators of the Dirac function, which are employed as relaxation kernels. Equations are constructed for determining the instantaneous modulus and the parameters of these functions from experimental stress-strain diagrams obtained at three different constant loading rates.Moscow Institute of Electronic Machine Building. Translated from Mekhanika Polimerov, No. 5, pp. 945–950, September–October, 1970.     

Method of successive approximations in the nonlinear theory of viscoelasticity

A method of successive approximations, a generalization of the Il'yushin method of elastic solutions, is proposed for solving problems of the nonlinear theory of elasticity in which the stress-strain relation is given in the form of a time operator Frechet-differentiable in a neighborhood of zero. The nonlinear relaxation kernels are found from the given nonlinear creep kernels for the principal quadratic theory of elasticity. These relations make it possible to formulate the boundary value problem for this theory. By way of illustration the problem of the pressure exerted on a space by a sphere is examined within the framework of the developed theory. The question of the convergence of the method is discussed in relation to the quadratic theory of visco-elasticity.Presented at the Third All-Union Conference on Theoretical and Applied Mechanics, Moscow (January, 1968).Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 236–242, March–April, 1969.     

Numerical methods in the theory of viscoelasticity

Formulas are given for calculating the coefficients of differential operators of defining equations on the basis of given approximations of the relaxation kernels in the form of the sum of exponential curves. As the defining equations it is suggested to use quadrature formulas into which are substituted the relaxation kernels found experimentally without preliminary analytic approximation. A three-dimensional difference problem of the linear isotropic theory of viscoelasticity is formulated. The direct and inverse -transformation establishing the correspondence between the viscoelastic and elastic difference problems is introduced. The specific characteristics of the use of the net, Ritz, finite-element, and variation-difference methods in solving problems of viscoelasticity theory are examined. A method facilitating the arrangement of the information on relaxation kernels in a computer memory is indicated.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 417–428, May–June, 1973.     

Determination of regular discrete relaxation spectra from the viscoelastic functions

A procedure for determining regular discrete relaxation spectra from the viscoelastic functions is presented as a generalization of a previously proposed procedure for determining the conditional rheological characteristics in a piecewise-exponential approximation of the experimental creep, relaxation, and – curves. The calculated data are in good agreement with the experimental results.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 801–807, September–October, 1971.     

Evaluation of integral operators of viscoelasticity

A method of calculating the integral operators of viscoelasticity from arbitrary continuous functions is proposed for the case where the relaxation (creep) function is given in tabulated or graphic form. The problem of constructing the creep function from an experimentally known relaxation function is solved.Moscow Institute of Electronic Machine Building. Translated from Mekhanika Polimerov, No. 6, pp. 1115–1117, November–December, 1973.     

Some relationships between the specific functions and constants of visoelastic media

It is proved that the shear, lateral creep, and relaxation functions can be expressed in an elementary way by the longitudinal creep and relaxation functions and the elasticity modulus of the bulk.I. M. Gubkin Moscow Institute of Petrochemical and Gas Industry. Translated from Mekhanika Polimerov, No. 5, pp. 810–814, September–October, 1973.     

Analysis of nonlinear polymer creep

The relaxation properties of polyethylene are analyzed. The nonlinear time-dependent stress-strain relations and the creep and relaxation equations are obtained from the experimental creep data. The analysis is based on an appropriate variant of the nonlinear memory theory with singular functions whose parameters, together with the modulus of elasticity, are determined by the method described in [1].Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 410–414, May–June, 1969.     

Estimation of the upper and lower bounds of solutions of the integral equations of viscoelasticity

The different methods of solving problems of viscoelasticity for hereditary media that employ Laplace transforms or exact solutions of integral equations for inaccurately approximated kernels inevitably introduce errors associated with the approximation and the inverse transformations. Accordingly, it is necessary to estimate the accuracy of these methods. It is shown that the kernels of the integral equations of viscoelasticity permit the estimation, with a certain accuracy, of upper and lower bounds directly for the solutions of these integral equations. In cases when the accuracy of the estimate is sufficient, there is no need to employ other methods of solution.Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 976–985, November–December, 1968.     

Shear creep of orthogonally reinforced spherofibrous composites

Our previous theory for the viscoelasticity of spheroplastics and two-phase structural models was used to construct stress creep and relaxation operators for shear of orthogonally reinforced spherofibrous composites. The operators were constructed using the Volterra principle, Rabotnov's fraction exponential kernels, and approximate analytical relationships for the integral composite characteristics. Operators were taken incorporating data on the rheonomic characteristics of the composite, components with hybrid, hollow, and other fiber types. Approximate formulas were obtained for operators convenient for studying stress creep and relaxation in elements of three-dimensional structures.A. A. Blagonravov Mechanical Engineering Institute, Russian Academy of Sciences, Moscow. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 770–779, November–December, 1996.     

Modelling the viscoelasticity of cell shape changes

In the theory of linear viscoelasticity, creep and relaxation functions are the important delay kernels in the stress-strain relations. Quite recently, a creep function power law has been obtained experimentally for an isolated living cell (on the scale of the cell). The corresponding form of the relaxation function is derived using the interconversion formula. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of the one-dimensional problem of nonlinear creep

A method of analyzing experimental creep curves of a nonlinear viscoelastic material to obtain relaxation curves is examined. It is assumed that the family of creep curves in question cannot be represented as a product of the stress function and a function of time. The investigation is carried out using the memory theory. The sum of the exponentials for curves not having a singularity at the start of the process is taken as the creep kernel [1]. A method of approximation by the sum of the exponentials is given. For processes with an initial singularity it is proposed to use the corresponding kernel, for which the resolvent is given.Mekhanika Polimerov, Vol. 2, No. 5, pp. 678–687, 1966     

Certain integral transforms with the Macdonald function Kν(z) in the kernels

Four integral transforms are considered with the Macdonald function in their kernels. Existence and inversion theorems are proved and Parseval equalities are established in a Hilbert space, in a Wiener normed ring, and in the space of generalized Gelfand-Shilov functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 990–993, July, 1990.     

Quasilinear theory of viscoelasticity and the small parameter method

A closed quasilinear quadratic theory of viscoelasticity is proposed for bodies with physical nonlincarity. All the basic unique relations between the stress and strain tensors and time are established. Time relations between the invariant characteristics of combined loading processes are given. Integral equations relating the secondary kernels of creep and relaxation are obtained, and their connection with the corresponding kernels of the linear theory is determined. The singular properties of the kernels are elucidated, and their principal parts are isolated. Examples of possible expressions for the secondary kernels are given, and their general properties are examined.Mekhanika Polimerov, Vol. 2, No. 2, pp. 170–189, 1966Read at the Riga Conference on Polymer Mechanics, 11 November 1965.     

Isolation of the principal part of memory influence functions for describing relaxation processes in the initial period

In order to describe relaxation processes-creep and relaxation-during a short initial period, the principal part of the influence functions is isolated in the form which generates Dirac delta functions. By means of the formulas constructed, the characteristics of viscoelastic media are determined from the data of relaxation or creep tests with allowance for the initial loading.Mekhanika Polimerov, Vol. 3, No. 4, pp. 625–635, 1967