ISSN (Print): 2224-9893 ISSN (Online): 2226-1869 | ||
Numerical simulation of an elastic tube containing a flowing fluid BOCHKAREV S.A., LEKOMTSEV S.V. Received: 03.06.2011 Published: 03.06.2011 ![]() Abstract:
The finite element method is applied to analyze natural vibrations and stability of cylindrical tubes interacting with inviscid compressible fluid. The motion of bodies of revolution is described in the framework of the linear theory of elasticity. The compressible media is considered in accordance with potential theory. The corresponding differential equation for the potential velocity perturbation is reduced to a system of equations using the Galerkin method. For pipe used variational principle of virtual displacements, which includes the linearized Bernoulli equation to calculate the hydrodynamic pressure exerted by the fluid on the elastic structure. Numerical simulation is based on the semianalytic finite-element method. The solution of the problem reduces to evaluation and analysis of the complex eigenvalues of the connected system of equations. The results are compared with known theoretical and experimental data for pipes containing stationary or flowing medium. The limits of applicability of different types of finite elements including the shell element have been determined. Keywords: classical theory of shells, cylindrical tube, linear theory of elasticity, potential compressible fluid, finite-element method, natural vibrations, stability, flutter, divergence.
Authors:
Lekomtsev Sergey Vladimirovich (Perm, Russia) – postgraduate, Institute of Continuous Media Mechanics UB RAS (614013, 1, Koroleva st., Perm, Russia, e-mail: lekomtsev@icmm.ru). Bochkarev Sergey Arkadyevich (Perm, Russia) – Candidate of Physical and Mathematical Sciences, Institute of Continuous Media Mechanics UB RAS (614013, 1, Koroleva st., Perm, Russia, e-mail: bochkarev@icmm.ru). References: . Bochkarev S.À., Matveenko V.P. Numerical investigation of boundary conditions on the dynamic behavior of cylindrical shells with flowing fluid [Chislennoe issledovanie vliyaniya granichnykh uslovij na dinamiku povedeniya tsilindricheskoj obolochki s protekayushhej zhidkost'yu]. Mechanics of Solids – Izvestiya RÀN. MTT, 2008, No. 3, P. 189–199. 2. Zhang Y.L., Gorman D.G., Reese J.M. Vibration of prestressed thin cylindrical shells conveying fluid. Thin-Walled Structures, 2003, No. 41, P. 1103–1127. 3. Zhang Y.L., Gorman D.G., Reese J.M. Finite element analysis of the vibratory characteristics of cylindrical shells conveying fluid. Comput. Methods Appl. Mech. Engng, 2002, Vol.191, P. 5207–5231. 4. Zhang Y.L., Gorman D.G., Reese J.M. A comparative study of axisymmetric finite elements for the vibration of thin cylindrical shells conveying fluid. Int. J. Numer. Meth. Engng, 2002, Vol.54, P. 89-110. 5. Zhang Y.L., Gorman D.G., Reese J.M. Vibration of prestressed thin cylindrical shells conveying fluid. Thin-Walled Struct, 2003, Vol. 41, P. 1103–1127. 6. Kochupillai J., Ganesan N., Padmanabhan C. A semi-analytical coupled finite element formulation for shells conveying fluids. Comput. Struct, 2002, Vol. 80, No. 3–4, P. 271–286. 7. Timoshenko S.P., Gudier D. Theory of elasticity [Teoriya uprugosti]. Moscow, 1975, 576 p. 8. Volmir À.S. Shells in the flow of liquid and gas. Problems of hydroelasticity [Obolochki v potoke zhidkosti i gaza. Zadachi gidrouprugosti]. Moscow, 1979, 320 p. 9. Zenkevich O. The finite element method in engineering [Metod konechnykh ehlementov v tekhnike]. Moscow, 1975, 256 p. 10. Lindholm U.S., Kana D.D., Abramson H.N. Breathing vibration of a circular cylindrical shell with an internal liquid. Journal of Aeronautical Science, 1962, Vol.29, P.1052–1059. 11. Païdoussis M.P., Denise J.-P. Flutter of thin cylindrical shells conveying fluid. Journal of Sound and Vibration, 1972, Vol.20, P. 9–26. Evaluation Of Matrix Mechanical Properties Around The Filler Particles In Polymer Nanocomposites With A Help Of Atomic Force Microscopy GARISHIN O.C., LEBEDEV S.N. Received: 03.06.2011 Published: 03.06.2011 ![]() Abstract:
Filled elastomers (rubber) are complex structurally inhomogeneous systems consisting of a mixture of dispersed particles, randomly distributed in the highly elastic polymer matrix (vulcanized rubber). Carbon black is most common as an active filler. Polymer nanolayers with special mechanical properties are formed on the surface of particles in the interaction of a binder and the active filler. The contribution of these nanolayers in the formation of rubber macro-properties can be quite substantial under certain conditions (nano-dispersed filler). Direct experimental study of polymer in nanolayers around the particles of carbon black in rubber involve significant technical difficulties due to the smallness of the objects of research and many additional distorting factors. The approach based on a combination of experimental studies of polymer nanolayers on a flat carbonized substrate by means atomic force microscopy and the corresponding model calculations was used to solve this problem. The estimation of stiffness and thickness of modified polymer was elaborated. These results do not contradict the known experimental data, indicating the prospects of this direction of research. Key words: polymer in nanolayers, elastomers, dispersed particles. Authors:
Garishin Oleg Konstantinovich (Perm, Russia) – Doctor of Physical and Mathematical Sciences, senior research assistant, Institute of Continuous Media Mechanics UB RAS (614013, 1, Koroleva st., Perm, Russia, Lebedev Sergey Nikolaevich (Perm, Russia) – Senior engineer, Institute of Continuous Media Mechanics UB RAS (614013, 1, Koroleva st., Perm, Russia, e-mail: gar@icmm.ru). References: 1. Perepechko I.I. Keeping in polymer physics [Vedenie v fiziku polimerov]. Moscow: Himija, 1978. – 312 p. 2. Gul V.E., Kuleznev V.N. Structure and mechanical properties of polymers [Structura i mehanichescie svoistva polimerov]. Moscow: Vysshaja shkola, 1982. – 320 p. 3. Grossberg A.Y., Khokhlov A.R. Statistical physics of macromolecules [Statisticheskaja fizika makromolekul]. Moscow: Nauka, 1989. – 344 p. 4. Wypych G. Handbook of Fillers, 2nd ed. Chem.Tec. Publishing, 1999. – 890 p. 5. Lipatov Y.S. Physical chemistry of filled polymers [Fizicheskaja himija napolnennyh polimerov]. Moscow: Himija, 1997. – 154 p. 6. Karasek L., Sumita M. Review: Characterization of dispersion state of filler and polymer-filler interactions in rubber carbon-black composites. Journal of materials science, 1996. – Vol. 31. – P. 281–289. 7. Fukahori Y. The mechanics and mechanism of the carbon black reinforcement of elastomers. Rub. Chem. Technol, 2003. – Vol. 76. – P. 548–565. 8. Morozov I., Svistkov A. Heinrich G., Lauke B. Computer modeling and examination of structural properties of carbon black reinforced rubber. Kautschuk Gummi Kunststoffe, 2006. – Vol. 59. – P. 642–647. 9. Morozov I.A. Garishin D.C., Volodin F.W., Kondyurin A.V., Lebedev S.N. Experimental and numerical modeling of elastomeric composites by investigating polyisoprene nanolayers on the carbon surface [Jeksperimental'noe i chislennoe modelirovanie jelastomernyh kompozitov putem issledovanija nanosloev poliizoprena na uglerodnoj poverhnosti]. Mechanics of composite materials and structures, 2008. – Vol. 14, No. 1. – P. 3–15. 10. Golovin Yu.I. Introduction to nanotechnology [Vvedenie v nanotehnologiju]. Moscow: Mashinostroenie, 2003. – 112 p. 11. Schuh C.A. Nanoindentation studies of materials. Materials Today, 2006. – Vol. 9, No. 5. – P. 32–40. 12. Bhushan B. Nanotribology and nanomechanics. Springer, 2005. – 1148 p. 13. Vanlandingham M.R., McKnicht S.H., Palmese G.R., Eduljee R.F., Gillepie J.W., McCulough Jr.R.L. Relating elastic modulus to indentation response using atomic force microscopy. Journal of Materials Science Letters, 1997. – Vol. 16. – P. 117–119. 14. Dao M., Chollacoop N., Van Vliet K.J., Venkatesh T.A., Suresh S. Computational modeling of the forward and reverse problems in instrumented indentation. Acta Mater, 2001. – Vol. 49. – P. 3899–3918. 15. Fischer-Cripps A.C. Nanoindentation and indentation measurements. Mater. Sci. Eng. 2004. – Vol. 44. – P. 91–102. 16. Timoshenko S.P. Theory of elasticity [Teorija uprugosti]. Moscow: Nauka, 1975. – 576 p. Chemical – mechanical polishing. Part 1. Main characteristic: review GOLDSTEIN R.V., OSIPENKO M.N. Received: 03.06.2011 Published: 03.06.2011 ![]() Abstract:
Chemical-mechanical polishing (CMP) is a perspective technology in fabrication of micro – and nanoelectronics elements, devices and systems. The development of models of CMP processes remains to be the actual problem. It is pointed out that known CMP models do not account for the features of chemical and mechanical mechanisms of interaction of active fluid and particles with a polished surface as well as an interaction of a viscoelastic pad with the surface. A description of the elementary acts of such interaction are absent in the available models. Keywords: chemical-mechanical polishing, abrasive, liquid, planarization, model. Authors:
Goldstein Robert Veniaminovich (Moscow, Russia) – corresponding member of the RAS, Doctor of Physical and Mathematical Sciences, Professor, Head of Laboratory A.Y. Ishlinsky Institute for Problem in Mechanics RAS (Moscow, pr.Wernadskogo, 101-1, goldst@ipmnet.ru, (495) 434-35-27). Osipenko Nikolay Michailovich (Moscow, Russia) – PhD in engng, Senior scientist, A.Y. Ishlinsky Institute for Problem in Mechanics RAS (Moscow, pr.Wernadskogo, 101-1, osipnm@mail.ru, (495) 434-43-14). References: 1. Zantye P.B., Kumar A., Sikder A.K. Chemical mechanical planarisation for microelectronics applications. Material Sci. and Engineering. 2004. – R. 45. – P. 89–220. 2. Jairath R. [and all] Chemical-mechanical polishing: process manufacturability. Solid State Technology. 1994. – No. 7. – Ð. 71–75. 3. Tseng W.-T. Polishing and material characteristics of plasma-enhanced chemically vapor deposited fluorinated oxide thin film. Journal of Electrochemical Society. 1997. – Vol. 144, No. 3. – P. 1100–1106. 4. Yasseen A.A., Mourlas N.J., Mehregany M. Chemical-mechanical polishing for polysilicon surface micromachining. Journal of Electrochemical Society. 1997. – Vol. 144, No. 1. – P. 237–242. 5. Worthington E. New CMP arhitecture address key process issues. Solid State Technology. 1996. – No. 1. – P. 61–62. 6. Bhushan M., Rouse R., Lukens J.E. Chemical-mechanical polishing in semidirect contact mode. Journal of Electrochemical Society. 1995. – Vol. 142, No. 11. – P. 3845–3851. 7. Ali I., Roy S.R., Shin G. Chemical-mechanical polishing of interlayer dielectric: A review. Solid State Technology. 1994. – ¹ 10. – P. 63–69. 8. Arnell R.D. Tribology principles and design applications. N.Y.: Springer-Verlag, 1991. – Chap. 5. – P. 124–160. 9. Runnels S.R. Feature-scale fluid-based erosion modeling for Chemical-Mechanical Polishing. Journal of Electrochemical Society. – 1994. – Vol. 141, No. 7. – P. 1900–1904. 10. Pietsch G.J., Chabal Y.J., Higashi G.S. Infrared-absorption spectroscopy of Si (100) and Si (111) surfaces after chemomechanical polishing. Journal of Applied Physics. 1995. – Vol. 78, No. 3. – P. 1650–1658. 11. Zhou L. Chemomechanical Polishing of silicon carbide. Journal of Electrochemical Society. 1997. – Vol. 144, No. 6. – P. L161–L164. 12. Cheng J.-Y. A novel planarization of oxide-filled shallow-trench isolation. Journal of Electrochemical Society. 1997. – Vol. 144, No. 1. – P. 315–320. 13. Pohl M.C., Griffiths D.A. The importance of particle size to the performance of abrasive particles in the CMP process. Journal of Electronic Materials, 1996. – Vol. 25, No. 10. – P. 1612–1616. 14. Smehalin K., Fertig D. Microscale dishing effect in a chemical mechanical planarization process for trench isolation. Journal of Electrochemical Society, 1996. – Vol. 143, No. 12. – P. 1281–1283. 15. Boyd J.M., Ellul J.P. Near-global planarization of oxide-filled shallow trenches using chemical mechanical polishing. Journal of Electrochemical Society, 1996. – Vol. 143, No. 11. – P. 3718–3721. 16. Boyd J.M., Ellul J.P. A one-step shallow trench global planarization process using chemical mechanical polishing. Journal of Electrochemical Society, 1997. – Vol. 144. – No. 5. – P. 1838–1841. 17. Cook L.M. Chemical processes in glass polishing. Journal of Non-Crystalline Solids, 1990. – Vol. 120. – P. 152–171. 18. Runnels S.R. Advances in physically based erosion simulators for CMP. Journal of Electronic Materials, 1966. – Vol. 25, No. 10. – P. 1574–1580. 19. Runnels S.R., Olavson T. Optimizing wafer polishing through phenomenological modeling. Journal of Electrochemical Society, 1995. – Vol. 142, No. 6. – P. 2032–2036. 20. Runnels S.R., Eyman L.M. Tribology analysis of chemical-mechanical polishing. Journal of Electrochemical Society, 1994. – Vol. 141, No. 6. – P. 1698–1701. 21. Warnock J. A two-dimensional process model for chemimechanical polish planarization. Journal of Electrochemical Society, 1991. – Vol. 138, No. 8. – P. 2398–2402. 22. Liu C.-W. Modeling of the wear mechanism during chemical-mechanical polishing. Journal of Electrochemical Society, 1996. – Vol. 143, No. 2. – P. 716–721. 23. Pietsch G.J., Higashi G.S., Chabal Y.J. Chemomechanical polishing of silicon: surface termination and mechanism of removal. Applied Physics Letters, 1994. – Vol. 64, No. 23. – P. 3115–3117. 24. Kneer E.A., Raghunath C., Raghavan S. Electrochemistry of chemical vapor deposited tungsten films with relevance to chemical mechanical polishing. Journal of Electrochemical Society, 1996. – Vol. 143, No. 12. – P. 4095–4100. 25. Kragelsky I.V., Dobychin M.N., Kombarov V.S. Friction and wear,calculation methods. N.-Y.:Pergamon Press, Ltd, 1982. – Chap. 11. – P. 352–366 26. Rajan K. Chemical-mechanical polishing of oxide thin films: The Rebinder-Westwood phenomenon revisited. Journal of Electronic Materials, 1996. – Vol. 25, No. 10. – P. 1581–1584. 27. Luo J., Dornfeld D.A. Material removal mechanism in chemical mechanical polishing: theory and modeling. IEEE transactions on semiconductor manufacturing, – Vol. 14, No. 2. – 2001. – P. 112–133. 28. Merchant T.R. Multiple scale integrated modeling of deposition processes. Thin Solid Films, No. 365. – 2000. – P. 368–375. 29. Lin Y.-Y., Chen D.-Y., Ma C. Simulations of a stress and contact model in a chemical mechanical polishing process. Thin Solid Films, No. 517. – 2009. – P. 6027–6033. Chemical – mechanical polishing. Part II. Model of local interactions GOLDSTEIN R.V., OSIPENKO M.N. Received: 03.06.2011 Published: 03.06.2011 ![]() Abstract:
On the base of the analytical review of the current state of the theory and problems of Chemical – mechanical polishing (CMP) modeling some approaches were suggested to the problem accounting for the complex of the phenomena of different scales determining the polishing rate such as diffusion of slurry into the surface layer and restriction of time of chemical treatment of the surface by a rough pad being under the action of a mechanical load. A model of the CMP process was developed. Within the framework of this model a dependence of the polishing rate on the loading parameters was derived. The dependence generalizes the empirical Preston law. Keywords: chemical-mechanical polishing, abrasive, liquid, planarization, model. Authors:
Goldstein Robert Veniaminovich (Moscow, Russia) – corresponding member of the RAS, Doctor of Physical and Mathematical Sciences, Professor, Head of Laboratory A.Y. Ishlinsky Institute for Problem in Mechanics RAS (Moscow, pr.Wernadskogo, 101-1, goldst@ipmnet.ru, (495) 434-35-27). Osipenko Nikolay Michailovich (Moscow, Russia) – PhD in engng, Senior scientist, A.Y. Ishlinsky Institute for Problem in Mechanics RAS (Moscow, pr.Wernadskogo, 101-1, osipnm@mail.ru, (495) 434-43-14). References: 1. Chemical-mechanical polishing. Part 1. The basic pattern; review. 2. Goldstein R.V., Osipenko N.M., Chemical-mechanical polishing. Process model. [Himiko-mehanicheskoe polirovanie]. Moscow: IPMeh Sciences. – Preprint ¹ 918. 2009. – 40 p. 3. Jairath R. Chemical-mechanical polishing: Process manufacturability. Solid State Technology, 1994. – No. 7. – P. 71–75. 4. Luo J., Dornfeld D.A. Material removal mechanism in chemical mechanical polishing: theory and modelling. IEEE transactions on semiconductor manufacturing, Vol. 14. – No. 2. – 2001. – P. 112–133. 5. Nanz G., Camilletti L.E. Modeling of chemical-mechanical polishing: a review. IEEE transactions on semiconductor manufacturing, Vol. 8. – No. 4. – 1995. – P. 382–388. 6. Steigerwald J.M., Murarka S.P., Gutman R.J. Chemical-mechanical planarization of microelectronic materials. N.Y.: John Wiley & sons, INC, 1997. – 324 p. 7. Zantye P.B., Kumar A., Sikder A.K. Chemical mechanical planarisation for microelectronics applications. Material Sci. and Engineering, 2004. – R. 45. – P. 89–220. 8. K. Johnson, Mechanics of contact interactions [Mehanika kontaktnogo vzaimodejstvija]. Mir, 1989. – 510 s. 9. Shi F.G., Zhao B. Modeling of chemical-mechanical polishing with soft pads. Applied Physics, A. 67. – 1998. – P. 249–252. 10. Moore, D. Fundamentals and applications triboniki [Osnovy i primenenija triboniki]. Springer-Verlag, 1978. – 487 p. 11. Bhushan M., Rouse R., Lukens J.E. Chemical-mechanical polishing in semidirect contact mode. J. Electrochemical Society, Vol. 142, No. 11. – 1995. – P. 3845–3851 12. Cherepanov G.P. The mechanics of brittle fracture [Mehanika hrupkogo razrushenija]. Moscow: Nauka, 1974. – 640 p. Nonlinear localized magnetoelastic waves EROFEYEV V.I., MALKHANOV A.O. Received: 03.06.2011 Published: 03.06.2011 ![]() Abstract:
System dynamic equations magnetoelasticity for rods, plates and elastic three-dimensional environment are to evolution equations with respect to the longitudinal strain. Demonstrated the possibility of the formation of intense space-localized magnetoelastic waves (solitary waves of strain in the rod; quasiplanar dimensional wave beams in a plate, three-dimensional quasiplanar wave beams in an elastic conductive medium). Keywords: magnetoelasticity, wave, nonlinearity, localization. Authors:
Yerofeev Vladimir Ivanovich (Nizhny Novgorod, Russia) – Doctor of physical and mathematical sciences, professor, deputy director on scientific work of A.A. Blagonravov Mechanical Engineering Institute, RAS (603024, 85, Belinsky's street, Nizhny Novgorod, e-mail: erf04@sinn.ru). Malhanov Alexey Olegovich (Nizhny Novgorod, Russia) – Candidate of physical and mathematical sciences, research assistant of A.A. Blagonravov Mechanical Engineering Institute, RAS (603024, 85, Belinsky's street, Nizhny Novgorod, e-mail: alexey.malkhanov@gmail.com). References: 1. Ambarcumjan S.A., Bagdasarjan G.E., Belubekjan M.V. Magnitouprugost of thin covers and plates [Magnitouprugost' tonkih obolochek i plastin]. Moskow: Nauka, 1977. – 272 p. 2. Bagdasarjan G.E., Danojan Z.N. elektromagnitouprugie of a wave [Jelektromagnitouprugie volny]. Erevan: Izd-vo EGU, 2006. – 492 p. 3. Novackij V. Electromagnetic effects in firm bodies [Jelektromagnitnye jeffekty v tverdyh telah]. Moskow: Mir, 1986. – 160 p. 4. Mozhen Zh. Mehanika of electromagnetic continuous environments [Mehanika jelektromagnitnyh sploshnyh sred]. Moskow: Mir, 1991. – 560 p. 5. Tzou H.S. Piezoelectric Shells. Dordrecht: Kluwer, 1993. – 480 p. 6. Rogacheva N. The Theory of Piezoelectric Plates and Shells. Boca Raton: CRC Press, 1994. – 260 p. 7. Selezov I.T., Korsunskij S.V. Non-stationary and nonlinear waves in electrospending environments [Nestacionarnye i nelinejnye volny v jelektroprovodjawih sredah]. Kiev: Naukova dumka, 1991. – 200 p. 8. Erofeev V.I., Zemljanuhin A.I., Katson V.M., Mal'hanov A.O. Nonlinear the localized longitudinal waves in a plate cooperating with a magnetic field [Nelinejnye lokalizovannye prodol'nye volny v plastine, vzaimodejstvujuwej s magnitnym polem]. Vychislitel'naja mehanika sploshnyh sred, 2010. – Vol. 3, No. 4. – P. 5–15. Solutions of rigid plane problems in the framework of inelastic endochronic theory at large deformations and rotations KADASHEVICH YU.I., POMYTKIN S.P. Received: 03.06.2011 Published: 03.06.2011 ![]() Abstract:
Method for solving of material behavior problems under rigid plane loadings in the framework of endochronic theory of inelasticity at large (finite) deformations and rotations is proposed. Some numerical examples are presented. The possibilities of introduced constitutive equations are demonstrated. Keywords: inelasticity, constitutive equations, endochronic theory, large deformations, rigid plane loading. Authors:
Kadashevich Yuliy Isaakovich (Saint-Petersburg, Russia) – Doctor of Physical and Mathematical Sciences, Professor, Saint Petersburg State Technological University of Plant Polymers (198095, 4, Ivana Chernyh st., Saint-Petersburg, Russia). Pomytkin Sergey Pavlovich (Saint-Petersburg, Russia) – Candidate of Physical and Mathematical Sciences, Ass. Professor, Saint Petersburg State Technological University of Plant Polymers (198095, 4, Ivana Chernyh st., Saint-Petersburg, Russia, e-mail: sppom@yandex.ru). References: 1. Pozdeev À.À., Trusov P.V., Nyashin Yu.I. Large elastic-plastic deformations: theory, algorithms, and applications [Bol'shie uprugo-plasticheskie deformatsii: teoriya, algoritmy, prilozheniya]. Moscow, Nayka, 1986, 232 p. 2. Levitas V.I. Large elastic-plastic deformation of materials under high pressure [Bol'shie uprugo-plasticheskie deformatsii materialov pri vysokom davlenii]. Kiev, 2000, 232 p. 3. Korobeynikov S.N. Nonlinear deformation of solids [Nelineynoe deformirovanie tverdykh tel]. Novosibirsk, 2000, 262 p. 4. Lubarda V.A. Elastoplasticity theory. CRC Press, 2002, 638 p. 5. Nemat-Nasser S. Plasticity: A treatise on finite deformation of heterogeneous inelastic materials. Cambridge University Press, 2004, 730 p. 6. Valanis K.C. The concept of physical metric in thermodynamics. Acta Mechanics, 1995, Vol. 113. – P. 169–175. 7. Khoei A.R., Bakhshiani A., Modif M. An endochronic plasticity model for finite strain deformation of powder forming processes. Finite Elements in Analysis and Design, 2003, Vol. 40, Is. 2. – P. 187–211. 8. Kadashevich Yu.I., Pomytkin S.P. New principles for establishing the governing equations of the endochronic theory of plasticity at finite deformations [Novye printsipy sostavleniya opredelyayushhih uravnenij ehndokhronnoj teorii plastichnosti pri konechnyh deformatsiyah]. Machines and devices of pulp and paper production – Mashiny i apparaty tsellyulozno-bumazhnogo proizvodstva, 1996. – P. 124–127. 9. Kadashevich Yu.I., Pomytkin S.P. A new look at the constructione theory of plasticity taking into account the finite deformation [Novyj vzglyad na postroenie ehndokhronnoj teorii plastichnosti pri uchete konechnykh deformatsij]. Nauchno-tekhnicheskie vedomosti SPbGPU – Scientific and technical statements SPbSPU, 2003, Vol. 33, No. 3. – P. 95–103. 10. Kadashevich Yu.I., Pomytkin S.P. Analysis of complex loading with finite strains on endochronic theory of inelasticity [Ànaliz slozhnogo nagruzheniya pri konechnykh deformatsiyakh po ehndokhronnoj teorii neuprugosti]. Prikladnye problemy prochnosti i plastichnosti. Metody resheniya – Applied problems of strength and ductility. Methods of solution. Moscow, 1998. – P. 72–76. 11. Kadashevich Yu.I., Pomytkin S.P. Meeting the challenges of soft and hard loading taking into account the large deformations in the endochronic theory of plasticity [Reshenie zadach myagkogo i zhestkogo nagruzheniya pri uchete bol'shikh deformatsij v ehndokhronnykh variantakh teorii plastichnosti]. Prikladnye problemy prochnosti i plastichnosti – Applied problems of strength and ductility, 2000, Vol. 63. – P. 30–35. 12. Brovko G.L. Material and spatial concepts of defining relations of deformable media [Material'nye i prostranstvennye predstavleniya opredelyayushhih sootnoshenij deformiruemyh sred]. Applied Mathematics and Mechanics – Prikladnaya matematika i mekhanika, 1990, Vol. 54, Is. 5. – P. 814–824. 13. Chernyh K.F. Introduction to the physically and geometrically nonlinear theory of cracks [Vvedenie v fizicheski i geometricheski nelinejnuyu teoriyu treshhin]. Moscow, Nayka, 1996. – 288 p. 14. Bell J.F. The experimental foundations of solid mechanics. 1971. – 813 p. 15. Bell J.F. The experimental foundations of solid mechanics. 1971. – 813 p. Factors of carrying over for the three-componental deformable alloy KNYAZEVA A.G., DEMIDOV V.N. Received: 03.06.2011 Published: 03.06.2011 ![]() Abstract:
Parities for the generalized forces, convenient for a conclusion of expressions for streams of heat and weight in deformable environments are presented. The detailed conclusion of the equations for streams is given on an example of binary and three-componental systems. On the basis of thermodynamics of irreversible processes and the theory of Onzagera it is shown that the number of independent factors of carrying over decreases at the account of symmetry of the generalized differential equations of a condition. Formulas for all factors of the carrying over, connecting them with independently defined parameters are given: in self-diffusion factors, in factors of concentration expansion and in factors Rubbish. Numerical estimations of factors are made. Keywords: diffusion, thermodiffusion, barodiffusion, thermodynamics of irreversible processes, carrying over factors, binary and three-componental systems. Authors:
Knyazeva Anna Georgievna (Tomsk, Russia) – Doctor of Physical and Mathematical Sciences, Professor, Chief Scientific Officer, National Research Tomsk Polytechnic University (634021, 2/4, Akademichasky pr., Tomsk, Russia, e-mail: anna-knyazeva@mail.ru). Demidov Valeriy Nikolaevich (Tomsk, Russia) – Candidate of Physical and Mathematical Sciences, Senior Researcher, Institute of Strength Physics and Materials Science SB RAS (634021, 2/4, Akademichasky pr., Tomsk, Russia, e-mail: vn_demidov@mail.ru). References: 1. Kolesnichenko À.V., Maksimov V.M. The generalized Darcy law of filtration as a consequence of Stefan-Maxwell relations for a heterogeneous environment [Obobshhennyj zakon fil'tratsii Darsi kak sledstvie sootnoshenij Stefana-Maksvella dlya geterogennoj sredy]. Mathematical Modeling – Matematicheskoe modelirovanie, 2001, Vol. 13, Is. 1, P. 3–25. 2. Vagner K. Thermodynamics of alloys [Termodinamika splavov]. Moscow, 1957, 179 p. 3. Gurov K.P. Phenomenological thermodynamics of irreversible processes (physical basis) [Fenomenologicheskaya termodinamika neobratimykh protsessov (fizicheskie osnovy)]. Moscow, Nauka, 1978, 128 p. 4. Kondepudi D., Prigogine I. Modern thermodynamics: from heat engine to dissipative structures, 1998, 506 p. 5. Besson J., Cailletaud G, Chaboche G.T. Non-linear mechanics of materials. Springer, 2009, 450ð. 6. Aouadi M. Generalized theory of thermoelastic diffusion for anisotropic media. J. of Thermal Stresses, 2008, Vol. 31, P. 270–285. 7. Knyazeva À.G. On the modeling of irreversible processes in materials with a large number of internal surfaces [O modelirovanii neobratimykh protsessov v materialakh s bol'shim chislom vnutrennikh poverkhnostej]. Physical mesomechanics – Fizicheskaya mezomekhanika, 2003, Vol. 6, Is. 5, P. 11–27. 8. Gurov K.P., Kartashkin B.À., Ugaste Yu.E. Interdiffusion in multi-metallic systems [Vzaimnaya diffuziya v mnogofaznyh metallicheskih sistemah]. Moscow, Nauka, 1981, 350 p. 9. Lupis C.H.P. Chemical thermodynamics of Materials / North-Holland, New York-Amsterdam – Oxford, 1989. 10. Ershov G.S., Majboroda V.P. Diffusion in molten steel [Diffuziya v metallurgicheskih rasplavah]. Kiev, 1990, 224 p. 11. Zajt T.V. Diffusion in metals. Processes of exchange places [Diffuziya v metallakh. Protsessy obmena mest]. Moscow, 1958, 382 p. 12. Physical quantities. Handbook, ed. Igor Grigoriev, E.Z. Meylihova [Fizicheskie velichiny. Spravochnik, pod red. I.S.Grigor'eva, E.Z. Mejlikhova]. Moscow, 1991, 1232 p. Mathematical modeling of plastic deformation of FCC materials under different strain rate KOLUPAEVA S.N., SEMENOV M.E., ROZHNOV A.I. Received: 03.06.2011 Published: 03.06.2011 ![]() Abstract:
The mathematical model of plastic deformation in FCC materials which including the system of differential equations of the balance of deformation defects and software package for its realization are described. The results of the research of plastic behavior in FCC metals under different strain rate are represented. Keywords: plastic deformation, FCC metals, mathematical modeling, dislocations, point defects. Authors:
Kolupaeva Svatlana Nikolaevna (Tomsk, Russia) – Doctor of Physical and Mathematical Sciences, Professor, vice-rector for automation, Tomsk State University of Architecture and Building (634003, 2, Solyanaya ploschad, Tomsk, Russia, e-mail: ksn58@yandex.ru) Semenov Michail Evgenyevich (Tomsk, Russia) – Candidate of Physical and Mathematical Sciences, Ass. Professor, Tomsk State University of Architecture and Building (634003, 2, Solyanaya ploschad, Tomsk, Russia, e-mail: vn_demidov@mail.ru) Rozhnov Alexandr Igorevich (Tomsk, Russia) – postgraduate, Rubtsovsk Industrial Institute (658207, 2/6, Traktornaya st., Rubtsovsk, Altay reg., Russia, e-mail: mydrawer@mail.ru) References: 1. Beilby G.T. The hard and soft states in metals. Journ. Inst. of Metals, 1911, Vol. 6, No. 5. 2. Bol'shanina M.À. Hardening and relaxation as the main phenomena of plastic deformation [Uprochnenie i otdykh kak osnovnye yavleniya plasticheskoj deformatsii]. Proceedings of the Academy of Sciences. Physical Series – Izv. ÀN SSSR. Ser. Fizicheskaya, 1950, Vol. 14, Is. 2, P. 223–231. 3. Nikitina À.N., Bol'shanina M.À. Effect of strain rate on softening of copper/ Studies on solid state physics [Vliyanie skorosti deformatsii na razuprochnenie medi / Issledovaniya po fizike tverdogo tela]. Moscow, 1957, P. 193–234. 4. Àkulov N.P. Discolations and plasticity [Dislokatsii i plastichnost’]. Minsk, 1961, 109 p. 5. Orlov A.K. Kinetics of dislocations / Theory of crystals defects, Prague: Publishing House of the Czechoslovak Academy of Sciences, 1966, P. 317–338. 6. Bergstrom J. A dislocation model for the stress strain behaviour of polycrystalline a-Fe with special emphasis on the variation of the densities of mobile and immobile dislocations. Mater. Sci. and Eng, 1970, Vol. 5, No. 4, P. 193–200. 7. Gilman D.D. Microdynamic theory of plasticity/Microplasticity [Mikrodinamicheskaya teoriya plastichnosti / Mikroplastichnost'] Moscow, 1972. P. 18–37. 8. Lagneborg R. Dislocation mechanisms in creep. Intern. Metals. Rev, 1972, Vol. 17, P. 130–146. 9. Essmann T., Mughrabi H. Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities. Phil. Mag. (a), 1979, Vol. 40, Nî. 6, P. 731–756. 10. Popov L.E., Kobytev V.P., Kovalevskaya T.À. Plastic deformation of alloys [Plasticheskaya deformatsiya splavov]. Moscow, 1984, 182 p. 11. Popov L.E., Kobytev V.P., Kovalevskaya T.À. The concept of hardening and dynamic recovery in the theory of plastic deformation [Kontseptsiya uprochneniya i dinamicheskogo vozvrata v teorii plasticheskoj deformatsii]. Proceedings of the higher education institutions. Physics – Izvestiya vuzov. Fizika, 1982, No. 6, P. 56–82. 12. Popov L.E., Pudan L.Ya., Kolupaeva P.N. Mathematical modeling of plastic deformation [Matematicheskoe modelirovanie plasticheskoj deformatsii]. Tomsk, 1990, 185 p. 13. Kolupaeva P.N., Starenchenko V.À., Popov L.E. Instability of plastic deformation of crystals [Neustojchivosti plasticheskoj deformatsii kristallov]. Tomsk, 1994, 301 p. 14. Popov L.E., Starenchenko V. À., Kolupaeva P. N. The dynamics of dislocations and shear deformation of crystals diffusion. Modeling in Mechanics [Dinamika dislokatsij i sdvigo-diffuzionnaya deformatsiya kristallov. Modelirovanie v mekhanike]. 1989, Vol. 3(20), No. 5, P. 93–117. 15. Kolupaeva P.N., Starenchenko V.À., Popov L.E. Instability of plastic deformation of crystals [Neustojchivosti plasticheskoj deformatsii kristallov]. Tomsk, 1994, 301 p. 16. Popov L.E., Kolupaeva S.N., Vihor N.A. Dislocation subsystem stability in f.c.c. materials under intensive loading. Computational Materials Science. 2000, No. 19 (1–4), P. 158–165. 17. Kolupaeva P.N., Erygina E.V., Kovalevskaya T.À., Popov L.E. A qualitative study of the evolution of the defect subsystem of incoherent heterophase alloys with hardening phase in the intensity of exposure [Kachestvennoe issledovanie ehvolyutsii defektnoj podsistemy geterofaznykh splavov s nekogerentnoj uprochnyayushhej fazoj pri intensivnykh vozdejstviyakh]. Physical Mesomechanics – Fizicheskaya mezomekhanika, 2000, Vol. 3, No. 2, P. 63–79. 18. Onipchenko T.V., Kolupaeva P.N., Starenchenko V.À. A qualitative study of models of formation of disoriented patterns of plastic deformation of fcc metals [Kachestvennoe issledovanie modeli formirovaniya razorientirovannykh struktur plasticheskoj deformatsii GTSK-metallov]. Physical Mesomechanics – Fizicheskaya mezomekhanika, 2000, Vol. 3, No. 6, P. 65–73. 19. Kolupaeva P.N., Komar' E.V., Kovalevskaya T.À. Mathematical modeling of strain hardening of dispersion-strengthened materials with the incoherent hardening phase [Matematicheskoe modelirovanie deformatsionnogo uprochneniya dispersno-uprochnennykh materialov s nekogerentnoj uprochnyayushhej fazoj]. Physical Mesomechanics – Fizicheskaya mezomekhanika, 2004. Vol. 7, Is. 1, P. 23–26. 20. Kolupaeva P.N., Novikova T.V., Starenchenko V.À. Mathematical modeling of the evolution of disoriented patterns of plastic deformation in copper and nickel [Matematicheskoe modelirovanie ehvolyutsii razorientirovannykh struktur plasticheskoj deformatsii v medi i nikele]. Bulletin of Tomsk State Architectural University – Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta, 2006, No. 1, P. 24–31. 21. Kolupaeva P.N., Semenov M.E., Puspesheva P.I. Mathematical modeling of temperature and velocity dependence of work hardening of fcc metals [Matematicheskoe modelirovanie temperaturoj i skorostnoj zavisimosti deformatsionnogo uprochneniya GTSK-metallov]. Deformation and Fracture of Materials – Deformatsiya i razrushenie materialov, 2006, No. 4, P. 40–46. 22. Popov L.E., Kolupaeva P.N., Sergeeva O.À. Crystallographic plastic strain rate. [Skorost' kristallograficheskoj plasticheskoj deformatsii]. Mathematical modeling of systems and processes – Matematicheskoe modelirovanie sistem i protsessov, 1997, No. 5, P. 93–104. 23. Kovalevskaya T.À., Danejko O.I., Kolupaeva P.N., Semenov M.E. Mathematical modeling of strain hardening of alloys containing dispersed non-deformable particles [Matematicheskoe modelirovanie deformatsionnogo uprochneniya splavov, soderzhashhikh nedeformiruemye dispersnye chastitsy]. Journal of Functional Materials – Zhurnal funktsional'nykh materialov, 2007, Vol. 1, Is. 3, P. 98–103. 24. Kolupaeva P.N. Simulation of temperature and velocity dependence of flow stress and deformation of the evolution of the defect in the medium of dispersion-strengthened materials [Modelirovanie temperaturnoj i skorostnoj zavisimosti napryazheniya techeniya i ehvolyutsii deformatsionnoj defektnoj sredy v dispersno-uprochnennykh materialakh] Bulletin of the Russian Academy of Sciences. Physics – Izvestiya RÀN. Seriya fizicheskaya, 2010, Vol. 74, No. 11, P. 1588–1593. 25. Semenov M.E., Kolupaeva P.N. Svidetel'stvo ob ofitsial'noj registratsii programmy SPFCC dlya EVM No. 20055612381. Zaregistrirovano v Reestre programm dlya EVM 12.09.2005 g. 26. Fridel J. Dislocations. Oxford, etc., Pergamon, 1964. 27. Larikov L.N., Yurchenko Yu.F. Thermal properties of metals and alloys [Teplovye svojstva metallov i splavov]. Kiev, 1985, 438 p. 28. Semenov M.E., Kolupaeva P.N. Analysis of regions of absolute stability of implicit methods for solving systems of ordinary differential equations [Ànaliz oblastej absolyutnoj ustojchivosti neyavnykh metodov resheniya sistem obyknovennykh differentsial'nykh uravnenij]. Proceedings of the Tomsk Polytechnic University – Izvestiya Tomskogo politekhnicheskogo universiteta, 2010, Vol. 317, No. 2, P. 16–22. 29. Semenov M.E., Kolupaeva P.N. Analysis of the effectiveness of the methods of Adams and Gere for solving stiff systems of ordinary differential equations package SPFCC [Ànaliz ehffektivnosti metodov Àdamsa i Gira pri reshenii zhestkikh sistem obyknovennykh differentsial'nykh uravnenij v pakete SPFCC]. Proceedings of the Tomsk Polytechnic University – Izvestiya Tomskogo politekhnicheskogo universiteta, 2011, Vol. 318, No. 5, P. 42–47. Profilogramms processing technique using wavelet-fractal analysis OPRYSHKO A.V., TARASOV M.Yu., UTKIN I.A., ANDREEV YU.S. Received: 15.05.2011 Published: 15.05.2011 ![]() Abstract:
Investigate the correlation between «evolutions of a dynamical system – the evolutions of the quality of the rubbing surfaces». An experiment was carried on friction machine «Tribal-2» for transfer the reciprocating motion with friction on the sample of brass. The internal dynamics of friction was investigated using multilevel wavelet decomposition and the calculation of fractal dimensions obtained profilogramms. After analysis of the data were obtained graphics describing the internal dynamics of the process: the evolution of the roughness parameters Ra, cumulates and Hurst coefficient for frequency component signals profilogramms. It was found that the Hurst exponent has an oscillatory character, which indicates to the oscillation stability and instability of the state of the surface layer of interacting counter-pairs Key words: friction, wavelet, fractal, Hurst coefficient, surface roughness, the spectral energy density, Tribal. Authors:
Opryshko Alexey Viktorovich (St.-Petersburg, Russia) – student of faculty of Exact mechanics and technologies of the St.-Petersburg state university of information technology, mechanics and optics (197101, St.-Petersburg, avenue Kronverksky, pr.49, e-mail: org@mail.ifmo.ru). Tarasov Michael Yurevich (St.-Petersburg, Russia) – master of faculty of Exact mechanics and technologies of the St.-Petersburg state university of information technology, mechanics and optics (197101, St.-Petersburg, avenue Kronverksky, pr.49, e-mail: org@mail.ifmo.ru). Utkin Ivan Anatolevich (St.-Petersburg, Russia) – master of faculty of Exact mechanics and technologies of the St.-Petersburg state university of information technology, mechanics and optics (197101, St.-Petersburg, avenue Kronverksky, pr.49, e-mail: org@mail.ifmo.ru). Andreev Yury Sergeevich (St.-Petersburg, Russia) – postgraduate student of faculty of Exact mechanics and technologies of the St.-Petersburg state university of information technology, mechanics and optics (197101, St.-Petersburg, avenue Kronverksky, pr.49, e-mail: org@mail.ifmo.ru). References: 1. Musalimov V. M, V.A.Dinamika's Jacks frictional nteractions [Dinamika frikcionnogo vzaimodejstvija], SPb., 2006. – 191 p. 2. Musalimov V.M., Sizova A.A., Ivanova E.K., Krylov N.A., Tkachev A.L. Osnovy triboniki, SPb., 2009. – 72 p. 3. Kalush J.A., Loginov V.M. Pokazatel Hurst and its hidden Properties [Pokazatel' Hersta i ego skrytye svojstva], the Siberian magazine of industrial mathematics. – 2002. – Vol, ¹ 4 (12). – P. 29–37. 4. Smolencev N.K. Osnovy teorii vejvletov. Vejvlety v MATLAB. – Kemerovo: Kemer. gos. un-t, 2003. – 200 p. Mathenatical model of micropolar anisotropic (orthotropic) elastic thin shells SARGSYAN S.H., FARMANYAN A.J. Received: 03.06.2011 Published: 03.06.2011 ![]() Abstract:
In this paper the general applied of micropolar elastic ortotropic thin shells is constructed on the basis of hypotheses method. Accepted hypotheses are formulated on the basis of qualatative results of the asimptotic solution of the boundary problem of micropolar theory of elasticity in thin regions. Keywords: micropolar, orthotropic, elastic, thin, shell, model. Authors:
Sarkisjan Samvel Oganesovich (Gyumri, Armenia) – Doctor of Physical and Mathematical Sciences, Armenian NAN corresponding member, Head of the Department, The Gyumri State Pedagogical Institute (377526, 4, Parujra-Sevaka st., Gyumri, Armenia, e-mail: afarmanyan@yahoo.com, slusin@yahoo.com). Farmanyan Ànait Zhoraevna (Gyumri, Armenia) – Candidate of Physical and Mathematical Sciences, Ass. Professor, Department of Mathematical Analysis and Differential Equations, The Gyumri State Pedagogical Institute (377526, 4, Parujra-Sevaka st., Gyumri, Armenia, e-mail: afarmanyan@yahoo.com, slusin@yahoo.com). References: 1. Eringen A. C. Theory of Mikropolar Plates. ZAMP, 1967, Vol. 18, Is. 1, P. 12–30. 2. Palmov V. À. Simplest consistent system of equations of the theory of thin elastic shells [Prostejshaya neprotivorechivaya sistema uravnenij teorii tonkikh uprugikh obolochek] Deformable Body Mechanics – Mekhanika deformiruemogo tela, Moscow, 1986, P. 106–112. 3. Zhilin P.À. Basic equations of non-classical theory of elastic shells [Osnovnye uravneniya neklassicheskoj teorii uprugikh obolochek]. Dynamics and Strength of Machines – Dinamika i prochnost' mashin, 1982, Vol. 386, P.29-42. 4. Shkutin A.I. Mechanical deformation of flexible bodies [Mekhanika deformatsij gibkikh tel]. Novosibirsk, 1988, 128 p. 5. Vanin G.À. Moment mechanics of thin shells [Momentnaya mekhanika tonkikh obolochek]. Mechanics of Solids – Izvestiya RÀN. MTT, 2004, No. 4, Ñ. 116–138. 6. Eremeev V.À., Zubov L.M. Mechanics of elastic shells [Mekhanika uprugikh obolochek]. Moscow, 2008, 280 p. 7. Rubin M.B. Cosserat Theories: Shells, Rods and Points. Dordrecht. Kluwer, 2000. 8. Neff P. A geometrically exact planar Cosserat shell-model with microstructure: existence of minimizers for zero Cosserat couple modulus. Math. Models Methods Appl. Sci., 2007, Vol. 17, Is. 3, P. 363–392. 9. Birsan M. On Saint-Venant’s principle in the theory of Cosserat elastic shells. Int. J. Eng. Sci., 2007, Vol. 45, Is. 2–8, P. 187–198. 10. Wang F.Y. On the solutions of Eringen’s micropolar plate equations and of ather approximate equations. Inter. J. Eng. Sci, 1990, Vol. 28, Is. 9, P. 919–925. 11. Altenbach H., Eremeyev V. A. On the linear theory of micropolar plates. ZAMM, 2009, Vol. 89, Is. 4, P. 242–256. 12. Sarkisjan S.O. Micropolar theory of thin rods, plates and shells [Mikropolyarnaya teoriya tonkikh sterzhnej, plastin i obolochek]. Proceedings National Academy of Sciences of Armenia. Mechanics – Izvestiya NÀN Àrmenii. Mekhanika, 2005, Vol. 58, No. 2, P. 84–95. 13. Altenbach J., Altenbach H., Eremeyev V. On generalized Cosserat-Type Theories of Plates and Shells: a Short Review and Bibliography. Arch. Appl. Mech. Special Issue, doi 10, 1007/s 00419-009-0365-3. 14. Sarkisjan S.O. Mathematical models of micropolar elastic thin beams [Matematicheskie modeli mikropolyarnykh uprugikh tonkikh balok] Doklady NÀN Àrmenii, 2011, Vol. 111, No. 2. 15. Sarkisjan S.O. General mathematical model of micropolar elastic thin plates [Obshhie matematicheskie modeli mikropolyarnykh uprugikh tonkikh plastin]. Proceedings National Academy of Sciences of Armenia. Mechanics – Izvestiya NÀN Àrmenii. Mekhanika, 2011, Vol. 64, No. 1, P. 58–67. 16. Sarkisjan S.O. The general theory of micropolar elastic thin shells [Obshhaya teoriya mikropolyarnykh uprugikh tonkikh obolochek] Physical mesomechanics – Fizicheskaya mezomekhanika, 2011, Vol. 14, Is. 1, P. 55–66. 17. Sarkisjan S.O. General dynamic theory of micropolar elastic thin shells [Obshhaya dinamicheskaya teoriya mikropolyarnykh uprugikh tonkikh obolochek] Doklady RÀN, 2011, Vol. 436, Is. 2, P. 195–198. 18. Sarkisjan S.O. Mathematical model of micropolar elastic thin shells with independent fields of displacements and rotations [Matematicheskaya model' mikropolyarnykh uprugikh tonkikh obolochek s nezavisimymi polyami peremeshhenij i vrashhenij]. Vestnik PGTU. Mehanika – Perm State Technical University Mechanics Bulletin, 2010, Is. 1, P. 99–111. 19. Novatskij V. Theory of elasticity [Teoriya uprugosti]. Moscow, 1975, 862 p. 20. Palmov V. À. Basic equations of asymmetric elasticity [Osnovnye uravneniya teorii nesimmetrichnoj uprugosti]. Applied Mathematics and Mechanics – Prikladnaya matematika i mekhanika, 1964, Vol. 28, Is. 3, P. 401–408. 21. Iesen D. Torsion of Anisotropic Micropolar Elastic Cylinders. ZAMM, 1974, Vol. 54, ¹12, P. 773–779. 22. Goldenvejzer À. L. Theory of thin elastic shells [Teoriya uprugikh tonkikh obolochek]. Moscow, 1953, 544 p. 23. Pelekh B.L. The theory of shells with finite shear rigidity [Teoriya obolochek s konechnoj sdvigovoj zhestkost'yu]. Kiev, 1973, 248 p. 24. Pertsev À.K., Platonov E.G. The dynamics of shells and plates (nonstationary problems) [Dinamika obolochek i plastin (nestatsionarnye zadachi)]. Leningrad, 1987, 316 p. 25. Grigorenko YA. M., Vaselenko À. T. Theory of shells of variable stiffness [Teoriya obolochek peremennoj zhestkosti]. Kiev, 1981, 544 p. Crystal plasticity theories and their applications to the description of inelastic deformations of materials. Part 3: Hardening theories, gradient theories TRUSOV P.V., VOLEGOV P.S. Received: 03.06.2011 Published: 03.06.2011 ![]() Abstract:
Provides an overview of a wide class of plasticity theories, known as crystal plasticity theories, based on the wording of constitutive relations, hypotheses and the main postulates of which lies in the consideration of explicit mechanisms of deformation at the meso- and microscale levels. The third part of the review is devoted to issues related to the mono- and polycrystals hardening description in existing crystal plasticity theories. Slip systems hardening in crystallites plays an extremely important role in crystal plasticity because largely determine the adequacy of this class of models. The models of generalized continua (including the gradient theory) are also considered. Keywords: review, crystal plasticity theories, hardening, dislocations, gradient theory, structural-analytic theory. Authors:
Trusov Petr Valentinovich (Perm, Russia) – Doctor of Physical and Mathematical Sciences, Professor, Head of Department of Mathematical Modeling of Systems and Processes, Perm State Technical University (614990, 29, Komsomolsky prospect, Perm, Russia, e-mail: tpv@matmod.pstu.ac.ru). Volegov Pavel Sergeevich (Perm, Russia) – Department of Mathematical Modeling of Systems and Processes, Perm State Technical University (614990, 29, Komsomolsky prospect, Perm, Russia, e-mail: crocinc@mail.ru). References: 1. Batdorf S.B., Budjanskij B.A. The relationship between stress and strain in the hardening metals to a complex stress state [Zavisimost' mezhdu napryazheniyami i deformaciyami dlya uprochnyayuwegosya metalla pri slozhnom napryazhennom sostoyanii] Mehanika – Mechanics, 1955, No. 5, P. 120–127. 2. Batdorf S.B., Budjanskij B.A. The mathematical theory of plasticity based on the concept of slipping [Matematicheskaya teoriya plastichnosti, osnovannaya na koncepcii skol'zheniya]. Mehanika – Mechanics, 1962, No. 1, P. 135–155. 3. Volegov P.S., Nikityuk A.S., Janz A.Yu. The geometry of the yield surface and hardening laws in crystal plasticity [Geometriya poverhnosti tekuchesti i zakony uprochneniya v fizicheskih teoriyah plastichnosti]. Vestnik PGTU. Matematicheskoe modelirovanie sistem i processov – Perm State Technical University Mathematical Modeling of Systems and Processes Bulletin, 2009, No. 17, P. 25–33. 4. Volegov P.S., Shulepov À.V. The elastic constants of single crystal in asymmetric crystal plasticity theory [Uprugie konstanty monokristalla v nesimmetrichnoj fizicheskoj teorii plastichnosti]. Vestnik PGTU. Mehanika – Perm State Technical University Mechanics Bulletin, 2010, No. 1, P. 19–34. 5. Volegov P.S., Yanz À.Yu. Asymmetric physical crystal plasticity theory of fcc polycrystals: a numerical implementation of some deformation schemes [Nesimmetrichnaya fizicheskaya teoriya plastichnosti GTSK-polikristallov: osobennosti chislennoj realizatsii nekotorykh skhem deformirovaniya]. Vestnik PGTU. Mehanika – Perm State Technical University Mechanics Bulletin, 2010, No. 1, P. 121–137. 6. Likhachev V.À., Malinin V.G. Structural – analytical theory of strength [Strukturno-analiticheskaya teoriya prochnosti]. Saint-Petersburg, 1993, 471 p. 7. McLin D. Mechanical properties of metals [Mekhanicheskie svojstva metallov]. Moscow, 1965, 432 p. 8. Belyaev S.P., Volkov À.E., Ermolaev V.À., Kamentseva Z.P., Kuz'min S.L., Likhachev V.À., Mozgunov V.F., Razov À.I., Khajrov R.Yu. Materials with shape memory effect [Materialy s ehffektom pamyati formy]. Saint-Petersburg, 1998. (Vol. 1 – 424 p., Vol. 2 – 374 p., Vol. 3 – 474 p., Vol. 4 – 268 p.). 9. Mirkin L.I. 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