Plastic deformation of models of a crystalline polymer in hydrostatic tension

The strength of a rhombic model of a defective polymer crystal in hydrostatic tension has been calculated for the set of configurations assumed by the model in the process of plastic deformation. The dislocation centers and twinning curves are calculated for models with one and two coordination polygons in hydrostatic tension. It is shown that in hydrostatic tension the twinning limit of the models is considerably reduced.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 20–25, January–February, 1976.     

Stability of strain gradient elastic bars in tension

Equilibrium of a bar under uniaxial tension is considered as optimization problem of the total potential energy. Uniaxial deformations are considered for a material with linear constitutive law of strain second gradient elasticity. Applying tension on an elastic bar, necking is shown up in high strains. That means the axial strain forms two homogeneously deformed sections in the ends of the bars and a section in the middle with high variable strain. The interactions of the intrinsic (material) lengths with the non linear strain displacement relations develop critical states of bifurcation with continuous Fourier’s spectrum. Critical conditions and post-critical deformations are defined with the help of multiple scales perturbation method. An erratum to this article can be found at     

The potential strain energy of a polymer molecule in nonlinear approximation

The intermolecular interaction mechanism is analyzed, and the results are used to derive a general semiempirical formula for the strain energy of a helical polymer molecule in nonlinear approximation. Formulas are given for the homogeneous straining of specific polymers. The relationship between the elastic constants of the molecule and the final strain is computed.Mekhanika Polimerov, Vol. 3, No. 4, pp. 608–614, 1967     

Analysis of stress and strain in tension cylindrical sample

One of the basic engineering problem occurring during the numerical analysis is to define the function of yield stress of material in the real conditions of a technological process. These properties are necessary to calculate the deformation and the state of stress and strain in the surface layer of an object. An inappropriate selection of the mechanical properties of the material is the reason of the occurrence of errors in numerical calculations of a continuous object, considered as a boundary and initial problem. Scientific investigations are being conducted with the aim to develop a database concerning yield stresses for different metals, depends on complex conditions of thermo-dynamical loads, e.g. temperature, the equivalent of the strain and the strain rate. The article presents a method of the determination of this dependence while using an experimental and numerical analysis. During the model investigations on the INSTRON testing machine, the force of elongation of the sample is measured and then calculations are made of the displacement of nodes of finite elements, plotted on outside surface of sample. The process is considered as a multi nonlinear problem. For this reason, an incremental method of motion and deformation of solid in an updated Lagrange formulation is used. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relations between the strain and stress tensors in successive biaxial tension

The manner of applying the load is one of the main factors governing the formation of the principal strains and their limiting values. Starting from the theory of local strains, relations between the strain and stress tensors are formulated for both simple and complex loading. It is shown that the principal strains associated with a given stress state vary depending upon the loading path.Mekhanika Polimerov, Vol. 1, No. 3, pp. 43–51, 1965     

Stress relaxation in physically nonlinear polymer materials under simultaneous tension and torsion

Conclusions 1. Application of our method of determining the parameters of physically nonlinear polymer materials from tests in uniaxial tension or in torsion ensures a satisfactory agreement between theoretical and experimental stress-relaxation curves corresponding to other modes of loading.2. Theoretical stress-relaxation curves for shear (tension) calculated on the basis of parameters which have been determined from approximations of stress-relaxation curves for tension (torsion) fall closely within the confidence interval for an individual measurement (with =95%).3. The agreement between theoretical and experimental stress-relaxation curves for a plane state of stress is 2–3 times worse, in terms of the mean-square relative difference, than the agreement between the respective curves for uniaxial tension.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 797–803, September–October, 1977.     

Hoop stress calculation for a nearly circular hole in a finitely deformed plate under plane strain and uniaxial tension

This work applies the theory of small deformations superposed on an exact finite solution (see Green/Zerna [2], Graham [7]) to discuss the plane strain deformation of a plate of incompressible Mooney-Rivlin material containing an almost circular hole and which is expanded by a radial pressure at this hole and uniaxial tension at infinity.As a specific example, we consider the theory as it applies to an elliptic hole of small eccentricity. The resulting differential equations are solved using Colsys [12, 13], a recent numerical technique for handling boundary value problems for families of ordinary differential equations, and graphs of hoop stress are drawn against finite extension for various values of eccentricity and uniaxial tension.

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Zusammenfassung Die vorliegende Arbeit wendet die Theorie der kleinen, einer exakten Lösung überlagerten, Deformationen an. um die ebene Verzerrung einer Platte aus inkompressiblem Mooney-Rivlin-Material zu diskutieren, die ein fast rundes Loch enthält und beansprucht wird durch Radialdruck an diesem Loch und einachsige Spannung im Unendlichen.Als spezielles Beispiel betrachten wir die Anwendung der Theorie auf ein elliptisches Loch mit kleiner Exzentrizität. Die resultierenden Differentialgleichungen werden durch Colsys [12, 13] gelöst. Dies ist eine neue numerische Methode, um Randwertprobleme für Familien von gewöhnlichen Differentialgleichungen zu lösen. Es werden Graphen der Tangentialspannung in Funktion der endlichen Dehnungen für verschiedene Werte von Exzentrizität und einachsiger Spannung aufgezeichnet.

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Visited Simon Fraser University during the academic year 1982/83.     

Development of slits in polyethylene and polypropylene films stressed in uniaxial tension

Optical microscopy has been used to investigate the development of a slit in polyethylene and polypropylene films with spherulites of different types and sizes stressed in uniaxial tension. The angle between the slit and the direction of extension was 0, 45, or 90°. Slits at 45 and 90° initially develop through localization of slits by a stronger oriented polymer and subsequently as a result of failure of the oriented polymer at the tip of the slit. A longitudinal slit does not develop and does not affect the deformation of the film.Mekhanika Polimerov, Vol. 3, No. 1, pp. 95–98, 1967     

Thermal effects in a glass laminate in tension

The results of a calorimetric investigation of a glass-reinforced textolite in uniaxial tension are presented. The specimens were deformed on the interval of strain rates from 0.3 to 10.5 mm/min at test temperatures from –30 to 80°C. The thermal effects are shown to depend on strain rate and test temperature.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 599–604, July–August, 1971.     

Strength of a viscoelastic liquid in quasistatic three-dimensional tension

Conclusions 1. An apparatus has been built with which experiments could be performed yielding, with a minimal spread of values, the quasistatic bulk strength of a liquid specimen.2. It has been established that the concentration of a polymer liquid does not significantly affect the experimental values of the liquid resistance to rupture. The strength of a viscous polymer liquid specimen is much lower than that of its low-viscosity solute.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 525–530, May–June, 1978.