Some fundamental problems of polymer mechanics

A survey of the present state of the science of polymer mechanics is presented with particular reference to the theory of linear and nonlinear viscoelasticity of homogeneous and heterogeneous polymers. Various approaches adopted in studies of this subject are discussed; these include methods based on the theory of creep of metals, on a statistical model composed of viscoelastic elements, and on the representation of functionals which, in a quite general sense, are sufficiently close to being linear.The second of these methods, which is approximate, yields results which always point to the nonlinearity of the properties of solids, even those that consist of linear elements. The third method is a natural generalization of the Boltzmann-Volterra theory.One of the fundamental tasks relating to the linear viscoelasticity of polymers is the application of the temperature-time analogy in studies of nonuniform and nonstationary problems of solids subjected to loading and heating-cooling cycles. The necessity of developing methods of modeling phenomena in solids of complex shape in nonuniform and nonstationary temperature and stress states (particularly in the nonlinear range) is discussed and a new method of solving problems of this type is described.Mekhanika Polimerov, Vol. 1, No. 3, pp 33–42, 1965     

General structural equilibrium solutions of boundary-value problems in the mechanics of composites

Based on the theory of R-functions, we have constructed general structural equilibrium solutions for stresses identically satisfying both the differential equilibrium equations and the contact conditions at the three-identically boundaries of inhomogeneities of arbitrary shape. These solutions can be used in developing the next generation of numerical and analytical methods in the mechanics of inhomogeneous bodies and the micromechanics of composite materials.Kharkov State Technical University of Construction and Architecture, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 474–481, July–August, 1997.     

Some aspects of the group-theoretic approach in problems of nonlinear mechanics

Two aspects of the application of the asymptotic decomposition method to the decomposition and investigation of nonlinear systems are considered. The first one is the extension of the class of functions in terms of which to form the asymptotic decomposition by applying special functions of mathematical physics. The other aspect is the extension of the asymptotic decomposition method to a new class of differential systems, namely, Pfaffian systems in involution.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 1, pp. 22–33, January, 1992.     

Some problems of heat conduction in transversally graded composites

The object of considerations is a two-component layer made of conductors non-periodically distributed in the form of laminas along the layer thickness. It is assumed that the distribution of the macroscopic properties of this laminate is approximated by continuous slowly-varying functions across laminas. Media of this kind can be treated as made of a functionally graded material. The aim of the paper is to apply the tolerance model, [8], to analyse one-directional, non-stationary heat conduction along the axis perpendicular to laminas. Moreover, received results are compared to the solutions obtained in the framework of the higher-order theory, [1]. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some mathematical problems related to the nonequilibrium statistical mechanics of infinitely many particles

This review article deals with mathematical problems related to the time evolution of systems of infinitely many particles. The probabilistic aspect of the obtained results is emphasized.Translated from Itogi Nauki i Tekhniki. Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 14, pp. 5–39, 1977.     

Pultrusion mechanics of fiber-reinforced thermoplastic composites

The associated problem of the rheology of a thermoplastic polymer melt during the pultrusion of fiber-reinforced composites in a plane-slotted die is resolved. The permeabilities of a stochastic fibrous system are determined for the case of a nonlinear (exponential) rheological model of the melt. The pressure distribution in the pultrusion tool is calculated with allowance for the permeability of the fibrous system. The dependence of the pultrusion force on the viscous properties of the melt and on the pull rate of the fibrous layer is established.Paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 547–554, July–August, 1995.     

Some problems in the application of statistical dynamics to shells manufactured from fibrous composites

On the basis of a statistical approach presupposing direct utilization of experimental data produced in modelling operations, a procedure is proposed for computational estimates on composite materials in which allowance is made for the initial defects, the variable properties of the material, and the conditions of use (physical medium). Experimental data on Plexiglas shells which confirm the practical applicability of the procedure are given. Questions relating to the design of tests on composite shells are discussed.Translated from Mekhanika Polimerov, No. 4, pp. 743–745, July–August, 1972.