Abstract
On the basis of the theory of similarity the author obtains a complete system of determining and nondetermining similarity criteria for the deformation theory of polymer plasticity in the simultaneous presence of hydrostatic pressure and a nonuniform temperature field. The determining criteria obtained make it possible to establish the necessary conditions for testing models so that the stress and strain fields are similar to the analogous field in the natural object. In this case the nondetermining criteria make it possible to transfer the stresses and strains measured on the model to the natural object. A similarity law generalizing the Kirpichev similarity law is obtained.
Similar content being viewed by others
References
T. Alfrey, Mechanical Behavior of High Polymers [Russian translation], Moscow, 1952.
A. E. Green and J. E. Adkins, Large Elastic Deformations and Nonlinear Continuum Mechanics [Russian translation], Moscow, 1965.
M. Reiner, Rheology [Russian translation], Moscow, 1965.
J. D. Ferry, Viscoelastic Properties of Polymers [Russian translation], Moscow, 1963.
A. A. Il'yushin, Plasticity [in Russian], Moscow, 1963.
V. N. Churakov, Aviatsionnaya tekhnika, 2, 40, 1965.
Collection: Mechanical Properties of Materials at Elevated Temperatures, ed. L. B. Getsov [in Russian], Moscow, 1965.
I. A. Birger, PMM,15, 765, 1951.
M. V. Storozhev and E. A. Popov, Theory of Metal Forming under Pressure [in Russian], Moscow, 1963.
Yu. N. Rabotnov, Strength of Materials [in Russian], Moscow, 1962.
S. D. Ponomarev et al., Strength Calculations in Machine Building, Vol. 2 [in Russian], Moscow, 1958.
S. B. Ainbinder, M. G. Laka and I. Yu. Maiors, Mekh. polim. [Polymer mechanics], 1, 65, 1965.
E. B. Trostyanskaya et al., New Materials in Technology [in Russian], Moscow, 1964.
G. L. Zodelava, E. N. Bogacheva, N. D. Gogokhiya, and G. A. Zukanov, Mekh. polim. [Polymer Mechanics], 1, 76, 1965.
L. I. Sedov, Similarity and Dimensional Methods in Mechanics [in Russian], Moscow, 1965.
G. Birkhoff, Hydrodynamics [Russian translation], Moscow, 1963.
A. A. Gukhman, Introduction to the Theory of Similarity [in Russian], Moscow, 1963.
S. S. Kutateladze and M. M. Borishanskii, Heat Transfer Handbook [in Russian], Moscow-Leningrad, 1959.
A. V. Luikov and Yu. A. Mikhailov, Theory of Heat and Mass Transfer [in Russian], Moscow-Leningrad, 1963.
M. V. Kirpichev and A. A. Gukhman, Tr. LOTI, 1, 1931.
K. Fink and C. Rohrbach, Handbuch der Spannungs- und Dehnungsmessung [Russian translation], Moscow, 1961.
A. Sobey, J. Roy. Aeronaut. Soc., 587, 646, 1959.
V. F. Yakovlev and I. S. Inyutin, Measurement of Stresses in Machine Parts [in Russian], Moscow-Leningrad, 1960.
I. S. Inyutin, Electric Strain Gage Measurements of Stresses in Plastics Parts [in Russian], Tashkent, 1961.
D. D. Chegodaev, Z. K. Naumova and Ts. S. Dunaevskaya, Fluoroplastics [in Russian], Leningrad, 1960.
A. F. Bermant, Mappings, Curvilinear Coordinates, Transformations, Green's Formulas [in Russian], Moscow, 1958.
K. I. Chernyak, Epoxy Compounds and Their Applications [in Russian], Leningrad, 1963.
G. S. Vardanyan and N. I. Prigorovskii, Izv. AN SSSR, Mekh. i mashinostr., 4, 146, 1962.
G. I. Pokrovskii and I. S. Fedorov, Centrifugal Modeling for Solving Engineering Problems [in Russian], Moscow, 1953.
A. A. Il'yushin, collection: Engineering Methods of Analyzing Technical Processes of Metal Forming Under Pressure [in Russian], Moscow, 1964.
V. L. Kirpichev, ZhRFKhO, Ser. fiz., 6, 9, 1874.
E. V. Kudryavtsev, K. N. Chakalev, and N. V. Shumakov, Nonstationary Heat Transfer [in Russian], Moscow, 1961.
Author information
Authors and Affiliations
Additional information
Mekhanika Polimerov, Vol. 3, No. 2, pp. 250–258, 1967
Rights and permissions
About this article
Cite this article
Churakov, V.N. Similarity criteria in the deformation theory of polymer plasticity. Polymer Mechanics 3, 167–172 (1967). https://doi.org/10.1007/BF00858856
Issue Date:
DOI: https://doi.org/10.1007/BF00858856