Deformation properties of polymers

The basic relations of the local strains theory are used to construct expressions for the deformation properties of polymers. The local strains function is assumed to be piecewise-linear, and nonlinear relations ₁₁(e₁₁) qualitatively describing the deformation of polymers are obtained.Mekhanika Polimerov, Vol. 1, No. 6, pp. 49–53, 1965     

Deformation and fracture of polymers

On the basis of experimental research it is suggested that in polymers under load two physically different kinetic processes — deformation and fracture — develop simultaneously. Their rates depend on different components of the stress tensor; accordingly, the relation between these rates can be experimentally controlled. It is suggested that these processes involve the overcoming of physically different potential barriers and that their elementary events embrace essentially different activation volumes. Deformation involves the overcoming of the forces of intermolecular interaction, and fracture, with the rupture of the main chains.Review of work carried out in the Materials Laboratory of the A. F. Ioffe Physico-Technical Institute, Academy of Sciences of the USSR.A. F. Ioffe Physico-Technical Institute, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 95–106, January–February, 1975.     

On weak convergence of random fields

We provide a characterization of compactness in the spaceD of functions of two variables defined on a unit square. The functions fromD have the property that their discontinuity points lie on smooth curves. Conditions for the tightness of probability measures inD and conditions for weak convergence of random fields with trajectories inD are derived. Vilnius Gediminas Technical University, Saulétekio 11; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 2, pp 169–184, April–June, 1999. Translated by R. Banys     

On weak convergence of random fields

We suggest simple and easily verifiable, yet general, conditions under which multi-parameter stochastic processes converge weakly to a continuous stochastic process. Connections to, and extensions of, R. Dudley’s results play an important role in our considerations, and we therefore discuss them in detail. As an illustration of general results, we consider multi-parameter stochastic processes that can be decomposed into differences of two coordinate-wise non-decreasing processes, in which case the aforementioned conditions become even simpler. To illustrate how the herein developed general approach can be used in specific situations, we present a detailed analysis of a two-parameter sequential empirical process.     

Crack tip fields in rubber-toughened polymers

Numerical simulations of the formation and the characteristic shape of plastic zones at crack tips in rubber-toughened polymers are performed in order to get a better understanding of the underlying micromechanisms. Complementing previous work, the present study focuses on the contribution of distributed crazing. A macroscopic constitutive model therefore has been developed that describes the overall effect of distributed crazing as an anisotropic flow process. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deformation of polymers under friction loading

A study has been made of the laws of distribution of elastic and residual deformations in the surface layers of polymers subjected to friction. The dependence of these deformations on normal pressure, sliding velocity, and duration of loading has been determined. A relation between deformation and antifriction characteristics has been established, and the relative effect of normal and tangential loads on surface-layer deformation determined.Mekhanika Polimerov, Vol. 3, No. 3, pp. 539–543, 1967     

Deformation properties of some glass-like polymers

Problems of deformation in amorphous, glass-like polymers are considered. The deformation and strength properties of PMMA (polymethyl methacrylate) were studied, for different temperatures and conditions of deformation. It was established that the long-term resistance to deformation of glass-like polymers subjected to forced elastic deformation, as judged by the time lapse to "neck" formation, is described by a longevity equation, allowance being made for the displacement of the origin with respect to the coordinates.Yu. V. Mirgorod participated in the experimental part of this work.Tambovsk Institute of Chemical Machine Construction and Experimental Laboratory of Polymer Physics, V. I. Lenin State Pedagogic Institute, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 717–720, July–August, 1972.     

Intensity of mechanical action and mechanical degradation of rigid polymers

The authors have investigated the relation between the degradation of rigid carbon-chain polystyrene, polyvinyl acetate, and polymethyl methacrylate polymers with the kinetics of mechanical degradation during vibromilling. They determine the critical value of the intensity necessary for the onset of the degradation process.Moscow Technological Institute of Light Industry. Translated from Mekhanika Polimerov, No. 2, pp. 362–364, March–April, 1974.     

Relaxation transitions in polymers in the presence of magnetic fields

A method of studying the effect of magnetic fields on polymeric materials has been developed. A universal cell has been designed for measuring the loss tangent in the presence of magnetic fields at different frequencies over a broad range of temperatures. The data obtained indicate that magnetic fields have an important effect on the loss tangents of polymeric materials and the location of the loss maximum on the tan -T temperature dependence.Sumgait Branch of the Mamedaliev Institute of Petrochemical Processes, Academy of Sciences of the Azerbaidzhan SSR. Translated from Mekhanika Polimerov, No. 4, pp. 611–614, July–August, 1971.     

Study of mechanical relaxation processes in ladder organosilicon polymers

Dynamic viscoelastic properties of ladder polyorganosiloxanes have been studied by the method of induced resonance oscillations in the temperature range from –150 to 300°C and in the frequency range from 8 to 300 Hz. Two broad maxima of mechanical losses were observed for all the polymers studied independently of their chemical structure, a low-temperature maximum in the –150 to 0°C region and a high-temperature maximum in the 0 to 250°C region. It was found that the introduction of alkyl groups into polyphenylsilsesquioxanes does not noticeably affect the position and nature of the low-temperature relaxation peaks but in certain cases leads to an increase in the dynamic modulus in polyphenylalkylsilsesquioxanes, compared with the modulus of polyphenylsilsesquioxane in the same temperature region. In the high-temperature region, a distinct dependence is observed of the relaxation peak on the length and the content of alkyl groups in the polymer. It has been found that increase in the length and the content of alkyl groups is accompanied by a shift in the peak in the direction of low temperatures and a decrease in the value of the modulus. Hypotheses have been suggested on the nature of the shifts which lead to the relaxation peaks observed in the ladder polyorganosiloxanes.Institute of Heteroorganic Compounds, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 804–809, September–October, 1973.     

On the weak topology of Banach spaces over non-archimedean fields

It is known that within metric spaces analyticity and K-analyticity are equivalent concepts. It is known also that non-separable weakly compactly generated (shortly WCG) Banach spaces over R or C provide concrete examples of weakly K-analytic spaces which are not weakly analytic. We study the case which totally differs from the above one. A general theorem is provided which shows that a Banach space E over a locally compact non-archimedean non-trivially valued field is weakly Lindelöf iff E is separable iff E is WCG iff E is weakly web-compact (in the sense of Orihuela). This provides a non-archimedean version of a remarkable Amir-Lindenstrauss theorem.     

Study of relaxation transitions in polymers in the presence of magnetic fields

Infrared spectroscopy in polarized light has been used to investigate specimens of polyvinyl chloride exposed to a magnetic field. It is shown that, depending on the conditions of heat treatment, various conformational transitions of the C-Cl bond occur in the polyvinyl chloride. The orientation effects in PVC exposed to a magnetic field are associated with the preferential formation of trans isomers of the C-Cl bond.Sumgait Branch, Mamedaliev Institute of Petrochemical Processes, Academy of Sciences of the Azerbaidzhan SSR. Translated from Mekhanika Polimerov, No. 5, pp. 923–925, September–October, 1972.     

Role of heating in connection with the reduced life of cyclically stressed polymers

An investigation of the effect of heating connected with cyclic deformation on the life of three polymer materials has shown that the measured heating cannot account for the experimentally observed reduction in fatigue life as compared with static loading.Mekhanika Polimerov, Vol. 4, No. 3, pp. 483–488, 1968     

Regularity of weak solution to Maxwell's equations and applications to microwave heating

In this paper we first study the regularity of weak solution for time-harmonic Maxwell's equations in a bounded anisotropic medium Ω. It is shown that the weak solution to the linear degenerate system, , is Hölder continuous under the minimum regularity assumptions on the complex coefficients γ(x) and ξ(x). We then study a coupled system modeling a microwave heating process. The dynamic interaction between electric and temperature fields is governed by Maxwell's equations coupled with an equation of heat conduction. The electric permittivity, electric conductivity and magnetic permeability are assumed to be dependent of temperature. It is shown that under certain conditions the coupled system has a weak solution. Moreover, regularity of weak solution is studied. Finally, existence of a global classical solution is established for a special case where the electric wave is assumed to be propagating in one direction.