Deformability modelling of foam elongation

The relationships concerning the deformation of rigid cellular foams during elongation are reviewed under the conditions of a monotonous load increase. The cellular structure behavior is modelled by the operation of a certain piston structure. The proposed equation leads to a satisfactory approximation of the experimental stress-strain diagram for polystyrene and poly(vinyl chloride) foams.V. A. Kucherenko Central Scientific-Research Institute of Building Constructions, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 154–157, January–February, 1972.     

Deformative properties of flexible plastic foams in compression

A calculation of the compression diagrams of flexible plastic foams during their long-time testing under a load is given on the basis of the proposed cell model, on the assumption that permanent set is related to buckling of the strands. The character of change of the nominal compressive strength and corresponding deformation as a function of the magnitude of permanent set is established. A marked change of the second section of the compression diagram (plateau), even to its degeneration, in the presence of considerable permanent set was found. A comparison of the experimental and calculated data showed their satisfactory correspondence.Vladimir Research Institute of Synthetic Resins. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 443–449, May–June, 1973.     

Effect of the cellular structure on thermal conductivity of rigid closed-cell foam polymers during long-term aging

The thermal conductivity of rigid closed-cell polyurethane foams during long-term aging has been studied. The similarity between the kinetics of changes in the physical and mechanical characteristics of PU foams on progressive aging is established, which is attributed to the effect of matrix destruction. It is found that rigid foams have cell walls of various strength, whose impact on the kinetics of changes in the physical characteristics of the foams during long-term aging is ascertained. The results of predicting the thermal conductivity of PU foams by the method of temperature-time analogy and establishing the limits of its application are discussed. The research presented is of interest both in determining the foam durability and in replacing freons by alternative, ecologically less harmful blowing agents.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 187–198, March–April, 1999.     

Radiation field of whispering gallery waves over a concave-convex boundary

In this work the wave field arising over a concave-convex reflecting boundary is studied in the Kirchhoff approximation. The field arises as a result of the incidence of whispering gallery waves on an inflection point of the boundary from the concave side. The shortwave asymptotics of the Kirchhoff integral are obtained which is expressed in terms of special functions in a neighborhood of the inflection point of the boundary and in a neighborhood of the tangent to the boundary at the inflection point. Diagrams are constructed that illustrate the behavior of the scattered field.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 49–65, 1981.     

Effect of cellular structure on the mechanical properties of plastic foams

A generalized equation for the compressive stress-strain diagrams of plastic foams is derived on the basis of a 14-faced model of the cell. The results obtained make it possible to predict the polymer base and type of cellular structure required to obtain a foam with predetermined mechanical properties in compression. The calculated values are shown to be in satisfactory agreement with the experimental data.Vladimir Scientific-Research Institute of Synthetic Resins. Translated from Mekhanika Polimerov, No. 4, pp. 594–602, July–August, 1970.     

Large Elastic Strains of Plastic Foams

The elastic deformation of plastic foams with a low (< 6%) volume fraction of solid phase is described based on a 4-rod equivalent element. A criterion is proposed which allows one to determine the parameter of structure of this element. Based on an analysis of the equivalent element, a procedure is developed for constructing the compression diagram of plastic foams in the region of large (> 70%) strains. The calculation results are compared with data found in the literature and experimental results for polyurethane foams obtained by the present authors. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 619–632, September–October, 2005.     

Elastic constants of monotropic plastic foams. 2. Deformation parallel to foam rise direction. Numerical calculations

In order to perform numerical calculations of the elastic constants of monotropic plastic foams with a pronounced strut-like structure, a package of computing programs has been developed. Numerical values of the elastic constants were determined using the Simpson method for the calculation of triple averaging integrals and stepwise unconditional minimization of the one-argument potential energy function. The parameters of the numerical calculation process providing acceptable accuracy of the results were evaluated. Dimensions of the structural elements in the model of isotropic plastic foams were determined and analyzed.Institute of Polymer Mechanics, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 163–172, March–April, 1998.     

Elastic constants of monotropic plastic foams. 3. Deformation parallel to foam rise direction. Analysis of the results

Based on an elaborate mathematical model shaped like an ellipsoidal cell, the Poisson's ratio v ₃₁ ^* and Young's modulusE ₃ ^* are calculated for monotropic (isotropic in the limiting case) plastic foams when loading parallel to the foam rise direction is considered and the hypothesis of half-axis is assumed. The effect of the state of the strut system on the calculation results is studied. The dependence of the calculated elastic constants on the characteristics of plastic foams such as the space filling coefficient, degree of anisotropy and knot parameter is analyzed. The theoretical results are compared with the experimental results as well as the results of other authors.Institute of Polymer Mechanics, University of Latvia, 23 Aizkraukles St., Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 823–838, November–December, 1998.     

Elastic constants of monotropic plastic foams. 1. Deformation parallel to foam rise direction. A mathematical model

A mathematical model of the deformative properties and structure of lightweight, monotropic (or isotropic in the limiting case) plastic foams with a pronounced strut-like structure has been elaborated in the linear theory of deformation. A selection of five independent elastic constants is described. For the integral characterization of the deformative properties of plastic foams as micrononhomogeneous composite materials, the elastic constants are introduced as the effective constants. In order to describe the plastic foam structure, a local model consisting of two parts is proposed, i.e., a model of a continuous medium for the calculation of stresses and a local structure model. Considering deformation parallel to the foam rise direction when the semiaxes hypothesis is assumed, the Young modulus and Poisson's ratio are determined.Institute of Polymer Mechanics. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 719–733, November–December, 1997.     

Effect of the third stress invariant on the characteristic curves of a material

The effect of the third invariant of the stress tensor (deviator) on the stress-strain intensity curve and the Lode diagram is investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 612–617, July–August, 1968.     

Short-wave scattering near the boundry inflection point

We investigate the problem of tangential incidence of short waves onto a surface with an inflection point. Formal solutions of the corresponding equation are constructed near the inflection point in the form of a quasihomogeneous function series. The formal solution is joined with the geometrical optics solution far from the inflection point of the boundary. The problem is restated as a scattering problem for the Schrodinger equation; existence, uniqueness, and smoothness theorems are proved. The formal asymptotic expansions are proved.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 148, pp. 152–166, 1985.In conclusion, I would like to thank M. M. Popov for suggesting the problem, and also V. M. Babich and M. M. Popov for useful comments.     

Whispering-gallery waves in a neighborhood of an inflection point of the boundary. Asymptotics of the wave field as t→∞

The asymptotics is constructed as t for the wave field generated by a whispering-gallery wave incident on an inflection point of the boundary. The asymptotics has ray character and is connected with the family of rays tangent to the convex part of the boundary beyond the point of inflection.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 140, pp. 151–166, 1984.     

Structural Modeling of the Mechanical Behavior of Periodic Cellular Solids: Open-Cell Structures

The numerical simulation of random cellular metals, e.g., metal foams, is still connected with many unsolved problems due to their stochastic structure. Therefore, a periodic model of cellular metals is developed and its mechanical behavior is investigated numerically under uniaxial and multiaxial stress states. The main advantage of the model is that a wide range of relative densities can be covered and that test specimens of the same geometry are possible to manufacture without oversimplifying their shape. The influence of different hardening behavior and different boundary conditions on the characteristics of the material is investigated. Furthermore, the effect of internal pore pressure on its uniaxial behavior and on the shape of yield surface are determined.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 405–422, May–June, 2005.     

Geometry of bifurcation diagrams

The geometry of a bifurcation diagram in the base of a versal deformation of a singularity is studied for single singularities on a manifold with boundary. In particular, vector fields and groups of diffeomorphisms are studied which are defined in a neighborhood of a bifurcation diagram as are stratification of a bifurcation diagram and decomposition of singularities.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Vol. 22, pp. 94–129, 1983.     

Concentration of the solutions near a limit ray in the neighborhood of an inflection point of the boundary

One considers the question regarding the energy concentration of a wave field in the neighborhood of a limit ray in the problem of the behavior of whispering gallery waves near an inflection point of the boundary. An estimate related to this question is proved.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 173, pp. 155–158, 1988.     

Movement of low-molecular-weight polyisobutylene in capillaries at large rates of deformation

Conclusions 1. A decrease in flow rate is observed upon increase in the pressure drop between the ends of a capillary at large pressure drops in the unstable flow region.2. It has been ascertained that the radial distribution of mean lengthwise velocity has an inflection close to the capillary wall.3. Wall slippage of the polymer has been observed and measured.4. A correlation of velocity pulsations in the channel with disturbances in the jet has been established.Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Moscow Power Institute. Translated from Mekhanika Polimerov, No. 4, pp. 724–730, July–August, 1976.     

Method of constructing shock compression diagrams for foam plastics

A method is proposed for constructing shock compression diagrams for foam plastics based on experimental determination of the residual deformation of a specimen after impact with a rigid obstacle. An approximate diagram is obtained for expanded polystyrene PS-1 of initial density 0.21 g/cm³, and the dynamic yield strength is estimated.Moscow. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 566–568, May–June, 1973.     

Correlation between static and fatigue strength of reinforced plastics

The conventional estimation of the fatigue strength of glass-fiber-reinforced plastics from the static strength in tension is shown to be inefficient by analysis of experimental data. It was found that a more reliable correlation is observed between their static and fatigue strengths as a result of referring _–1 to *, where * is the smaller of the stresses in tension or compression, determined from the inflection points on the static deformation curves. Views are expressed on the use of the correlation found for reducing the amount of fatigue tests.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 468–474, May–June, 1973.     

The scattering problem for the Schrödinger equation with a potential linear in time and in space. II. Correctness,smoothness, behavior of the solution at infinity

We study the scattering problem associated with the behavior of whispering gallery waves near the inflection point of the boundary. In order to solve the scattering problem, we prove the theorems of existence, uniqueness and smoothness of the solution. The formal asymptotic behavior is justified for t– and superexponential smallness of the wave field in the shadow zone is proved.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 148, pp. 13–29, 1985.     

Study of the role of intermolecular interactions (hydrogen bonds) in the initial stage of orientation of polyvinyl alcohol and vinyl alcohol copolymers

The effect of hydrogen bond rupture on the process of destruction of the starting crystallite structure of polyvinyl alcohol and copolymers of vinyl alcohol and N-vinylpyrrolidone and -vinylcaprolactam has been investigated. The differential spectrum method is used to establish the frequency (3200 cm^–1) of the band corresponding to the vibrations of the bound hydroxyl groups; the temperature dependence of the optical density of the 3200 cm^–1 band has been recorded. The strength of the starting structure is calculated from the stress-strain diagram and its temperature dependence is plotted. It is concluded that the strength of the starting structure is chiefly determined by the presence of hydrogen bonds between the polymer macromolecules.Leningrad Kirov Institute of Textile and Light Industry. Translated from Mekhanika Polimerov, No. 2, pp. 327–329, March–April, 1971.