Nonlinear stress-strain relations for carbon-reinforced plastics under continuous static loading

The specific characteristics of oriented reinforced polymers are quite fully taken into account by a nonlinear anisotropic theory of the same type as the nonlinear theory of elasticity or the deformation theory of plasticity, based on the use of tensor-linear relations containing two quadratic forms of the stress components without the introduction of higher-order tensors. The possibility of extending this theory to the case of uniaxial deformation of carbon-reinforced composites is demonstrated.Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 49–53, January–February, 1976.     

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.     

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.     

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.     

Correspondence principle and the method of approximations for certain nonlinear hereditary media

Problems for two classes of nonlinear hereditary media are reduced by integral transforms to problems of the nonlinear theory of elasticity. An approximation of the elastic solution that makes it possible to solve the formulated problems for nonlinear hereditary materials is demonstrated in the case when the viscoelastic problems reduce to problems of the theory of small elastoplastic strains with active loading.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 66–73, January–February, 1971.     

Nonlinear dynamical problem of a cyclinder with a slowly changing internal boundary

The problem of a hollow viscoelastic cylinder enclosed in an elastic shell is examined. The inside diameter varies. A nonlinear cubic theory is used to describe the relation between the stresses and strains in time. A vibration analysis is carried out for variable internal pressure.Moscow Institute of Electronic Machine Building. Translated from Mekhanika Polimerov, No. 2, pp. 274–280, March–April, 1973.     

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.     

Investigation of nonlinear properties of composites consisting of linear-elastic components

Problems of meridionally axisymmetrical geometrically nonlinear elasticity theory [2] are discussed as applied to the investigation of the properties of composites.Physicotechnical Institute, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 898–905, September–October, 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.     

Calculation of the nonlinear viscoelastic oscillations of an antivibration layer

It is proposed to use a viscoelastic layer to protect equipment against vibration. The principal quadratic theory of hereditary viscoelasticity is used as the physical relation between the forces and displacements. The solutions obtained for the integrodifferential vibration equation make it possible to minimize the displacements and accelerations of the protected equipment.Moscow Institute of Electronic-Machine Building. Translated from Mekhanika Polimerov, No. 2, pp. 321–326, March–April, 1972.     

Use of the results of auxiliary experiments in solving problems in the linear theory of viscoelasticity

The approximate method of solving problems of the theory of linear viscoelasticity with arbitrary creep and relaxation kernels, proposed in [2], is substantiated and generalized. The essence of this method consists in the approximation of the functions depending on the Laplace — Carson transforms of the mechanical characteristics of a viscoelastic body by means of certain combinations of the transforms of the creep and relaxation kernels. The expressions obtained as a result of the approximation enable the inverse transforms of the unknown functions to be found without difficulty.Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 963–969, November–December, 1968.     

Investigation of the anisotropy of the properties of glass-reinforced plastic shells

The load-carrying capacity and deformation of cylindrical and conical glass-reinforced plastic (ÉDT-10 resin) shells loaded in axial compression have been investigated experimentally in relation to the orientation of the fabric reinforcement. The results of the tests are compared with the relations of the theory of elasticity of an orthotropic body.Zhukovskii Central Aerohydrodynamics Institute, Moscow Region; Scientific Research Institute of Production Technology and Organization, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 814–818, September–October, 1969.     

Solution of the problems of a perforated disk,a conical bar,and a flat wedge of nonlinear viscoelastic material in pure shear,torsion, and bending,respectively

Exact solutions and approximations have been obtained for the problems of a disk with an opening twisted by opposite moments uniformly distributed over the inner and outer surfaces and of a conical bar twisted by a moment applied at the vertex of the cone. An approximate solution has been found for the problem of a flat wedge bent by pressure uniformly distributed along one of its sides. The disk is made of nonlinear viscoelastic material. In [1] it was proposed that problems for such a material be solved by the method of approximations. The rheological law of the nonlinear viscoelastic material of the cone and the wedge in Laplace—Carson transforms is the relation of the theory of small elastoplastic deformations with a power law of strain hardening.Institute of Electronic Engineering, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1071–1076, November–December, 1971.     

Nonlinear creep of TS8/3-250 glass-reinforced plastic

The creep and recovery of a glass-reinforced plastic are investigated within the frame-work of a nonlinear hereditary model. The material characteristics are determined for the three principal directions. The proportionality of the kernels is established.State Scientific-Research Institute of Machine Science, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 391–397, May–June, 1971.     

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.     

Method of solving equations of motion of viscoelastic media

A new method is proposed for solving dynamic problems for viscoelastic media based on the introduction of potential functions and transformation of equations of motion. The equations obtained for potential functions are used for constructing the general solution in the case of the effect of moving loads on viscoelastic media with plane-parallel interfaces. The problem of the propagation of Rayleigh surface waves is solved independently of the form of the kernels of the linear operators; a formula is obtained for determining the velocity of the Rayleigh surface wave with an arbitrary form of the viscoelastic operators. A method of experimental determination of the kernels determining the linear viscoelastic operators is proposed.V. V. Kuibyshev Moscow Civil Engineering Institute. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 429–435, May–June, 1973.     

Some fundamental problems of the theory of thermoviscoelasticity

Methods of solving quasistatic problems of the linear theory of thermoviscoelasticity are discussed. Special attention is given to the method of approximations. Modern methods of solving contact problems with a variable boundary and problems with a time-dependent boundary are briefly reviewed. Methods of solving problems with a nonuniform temperature field are outlined. The basic relations of the nonlinear theory of thermoviscoelasticity are given. Its various modifications and simplifications associated with the introduction of fairly general assumptions are examined. Methods of solving problems in certain nonlinear theories are noted. Nonisothermal (coupled) problems of thermoviscoelasticity and questions relating to the general theory with physical and geometric nonlinearity are discussed.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 41–58, January–February, 1971.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

Transition functions of the Il'yushin approximation method

Transition functions are constructed whose direct substitution for combinations of elastic constants in solutions of problems of elasticity theory permits writing the solution of the corresponding viscoelastic problems. Examples of using the transition functions for obtaining solutions of viscoelastic problems are given: circularly symmetric solid and anular plates, plate with a small circular hole, and viscoelastic half-plane loaded by a concentrated force.M. M. Gubkin Moscow Institute of the Petrochemical and Gas Industry. Moscow Institute of Electronic Engineering. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 405–416, May–June, 1973.     

Conditions for the design of shock-absorbing and vibration-proofing systems

The regions are given for the parameters of shock-absorbing and vibration-proofing systems leading to final overloads that do not exceed the design values. Shock-absorbing and vibration-proofing systems are considered as viscoelastic systems with hereditary properties. The stresses and displacements of the system as a function of time are based on the linear theory of Boltzmann and Volterra, and on the nonlinear main square theory of Ilyushin. The nucleus which characterizes the viscoelastic properties of the system is assumed to be singular; the regions of parameter variation of this function, obtained by minimization of the vibration overloads, represent the solution of the problem.Moscow Institute of Electronic Mechanical Engineering. Translated from Mekhanika Polimerov, No. 6, pp. 1029–1034, November–December, 1972.