THE NUMERICAL ANALYSIS OF THE EXPERIMENTAL SCHEMES ON DETECTION OF COUPLE-STRESS EFFECTS UNDER STATIC AND DYNAMIC EXTERNAL FORCES

Authors

  • V.V. Korepanov Институт механики сплошных сред УрО РАН

DOI:

Keywords:

Cosserat continuum, asymmetric elasticity theory, numerical solutions, experimental schemes, couplestress effects

Abstract

The paper presents the historical aspects of the theory of Cosserat continuum and the main stages of its development. The features of the theory and main stages was considered and associated of the development of experimental schemes to detect the couple-stress effects on the basis of solving two- and three-dimensional problems in the context of the asymmetric elasticity theory. First results of such experiments raised a number of issues related to the corresponding mathematical problem and its experimental analogue. In this regard, there was a problem of a broad series of numerical investigations aimed at assessing the impact of various factors in the making of operative embodiment, loading scheme and the choice of material to the level of quantities measured in the experiment. Such investigations allow us to estimate the prospects of future experiments aimed to identification the facts of the couple-stress behavior of materials under static and dynamic external influences.

Supporting Agencies
Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (№ 11-01-96022) и в рамках программы УрО РАН № 12-С-1-1015.

Author Biography

  • V.V. Korepanov, Институт механики сплошных сред УрО РАН
    кандидат физико-математических наук, научный сотрудник

References

  1. Cosserat E. et F. Theorie des corps deformables. - Paris: Librairie Scientifique A. Hermann et Fils, 1909. - 226 p.
  2. Erofeev V.I. Brat’a Kossera i mehanika obobsennyh kontinuumov // Vycisl. meh. splos. sred. - 2009. - T. 2. - No 4. - S. 5-10.
  3. MacCullagh J. An essay towards a dynamical theory of crystalline reflection and resraction // Trans. Roy. Irish. Acad. Sci., 1839. - Vol. 21. - P. 17-50.
  4. Thomson W. Mathematical and physical papers, 1882-1911. - 6 vols. - Cambridge University Press.
  5. Grekova E.F., Zilin P.A. Sreda Kel’vina i ferromagnetiki: opredelausie uravnenia i volnovye processy // Nelinejnaa akustika tverdogo tela: sb. nauc. tr. / pod red. V.I. Erofeeva. - N. Novgorod: Intelservis, 1998. - S. 87-90.
  6. Aero E.L., Kuvsinskij E.V. Osnovnye uravnenia teorii uprugosti s vrasatel’nym vzaimodejstviem castic. // Fizika tverdogo tela. - 1960. - T. 2. - Vyp. 7. - C. 1399-1409.
  7. Mindlin R.D. Vlianie momentnyh naprazenij na koncentraciu naprazenij // Mehanika: Sb. per. - M.: Mir. - 1964. - No 4. - S. 115-128.
  8. Pal’mov V.A. Osnovnye uravnenia teorii nesimmetricnoj uprugosti // PMM. - 1964. - T. 28. - Vyp. 3. - S. 401-408.
  9. Tupin R.A. Teorii uprugosti, ucityvausie momentnye naprazenia // Mehanika: sb. per. - 1965. - No 3. - S.113-140.
  10. Nowacki W. Couple-stresses in the theory of thermoelasticity // Bull. Acad. Polon. Sci. Ser. Sc. Techn. - 1966. - Vol. 14. - P. 505-512.
  11. Zubov L.M. Nonlinear theory of dislocations and disclinations in elastic bodies. - Berlin: Heidelberg; N.Y.: Springer, 1997. - 205 p.
  12. Nikitin E., Zubov L.M. Conservation lawsand conjugate solutions in the elasticity of simple materials and materials with couple stress // J. Elasticity. - 1998. - Vol. 51. - No 1. - P. 1-22.
  13. Erofeev V.I., Kazaev V.V., Semerikova N.P. Makromehaniceskoe modelirovanie uprugoj i vazko- uprugoj sred Kossera // Vycisl. meh. splos. sred. - 2009. - T. 2. - No 2. - S. 40-47.
  14. Lalin A.E., Pirozkov V.A,. Stepanov R.D. O rasprostranenii poverhnostnyh voln v srede Kossera // Akust. zurnal. - 1982. - T. 28. - No 6. - S. 838-840.
  15. Kules M.A., Matveenko V.P., Sardakov I.N. Postroenie i analiz analiticeskogo resenia dla poverhnostnoj volny Relea v ramkah kontinuuma Kossera // PMTF. - 2005. - T. 46. - No 4. - S. 116-124.
  16. Kules M.A., Matveenko V.P., Sardakov I.N. O rasprostranenii uprugih poverhnostnyh voln v srede Kossera // DAN. Mehanika. - 2005. - T. 405. - No 2. - S. 196-198.
  17. Kules M.A., Matveenko V.P., Sardakov I.N. O rasprostranenii uprugih poverhnostnyh voln v srede Kossera // Akust. zurnal. - 2006. - T. 52. - No 2. - S. 227-235.
  18. Kules M.A., Matveenko V.P., Sardakov I.N. Postroenie analiticeskogo resenia volny Lemba v ramkah kontinuuma Kossera // PMTF. - 2007.- T. 48. - No 1. - S. 143-150.
  19. Kules M.A., Matveenko V.P., Sardakov I.N. Dispersia i polarizacia poverhnostnyh voln Relea dla sredy Kossera // Izv. RAN. MTT. - 2007. - No 4. - S. 100-113.
  20. Analiz volnovogo resenia uravnenij elastokinetiki sredy Kossera v slucae ploskih ob"emnyh voln / M.A. Kules, V.P. Matveenko, I.N. Sardakov, M.V. Ulitin // PMTF. - 2008. - No 2. - S. 196-203.
  21. Nikolaevskij V.N. Geomehanika i fluidomehanika. - M.: Nedra, 1996. - 447 s.
  22. Khurana A., Tomar S.K. Longitudinal wave response of a chiral slab interposed between micropolar solid half-spaces // Int. J. Solids Struct. - 2009. - No 46. - P. 135-150.
  23. Khurana A., Tomar S.K. Transmission of longitudinal wave at a plane interface between micropolar elastic and chiral solid half-spaces: Incidence from micropolar half-space // J. of Sound and Vibration. - 2008. - No 311. - P. 973-990.
  24. Tomar S.K., Khurana A. Elastic waves in an electro-microelastic solid // Int. J. Solids Struct. - 2008. - No 45. - P. 276-302.
  25. Tomar S.K., Khurana A. Reflection and transmission of elastic waves from a plane interface between two thermo-microstretch solid half-spaces // Int. J. of Appl. Math. Mech. - 2009. - No 5 (4). - P. 48-68.
  26. Sadovskaa O.V. Cislennoe resenie prostranstvennyh dinamiceskih zadac momentnoj teorii uprugosti s granicnymi usloviami simmetrii // Zurn. vycisl. matematiki i matemat. fiziki. - 2009. - T. 49. - No 2. - S. 313-322.
  27. Korepanov V.V., Kules M.A., Matveenko V.P., Sardakov I.N. Analiticeskie i cislennye resenia staticeskih i dinamiceskih zadac nesimmetricnoj teorii uprugosti // Fiziceskaa mezomehanika. - 2007. - T. 10. - No 5. - S. 77-90.
  28. Korepanov V.V., Matveenko V.P., Sardakov I.N. Cislennoe issledovanie dvumernyh zadac nesimmetricnoj teorii uprugosti // Izv. RAN. MTT. - 2008. - No 2. - S. 63-70.
  29. Analiticeskie i cislennye resenia v ramkah kontinuuma Kossera kak osnova dla postanovki eksperimentov po obnaruzeniu momentnyh effektov v materialah / V.V. Korepanov, M.A. Kules, V.P. Matveenko, I.N. Sardakov // Vycisl. meh. splos. sred. - 2009. - T. 2. - No 4. - S. 76-91.
  30. Korepanov V.V., Matveenko V.P., Shardakov I.N. Finite element analysis of two- and three-dimensional static problems in the asymmetric theory of elasticity as a basis for the design of experiments // Acta Mech. - 2012. - Vol. 223. - No 8. - P. 1739-1750.
  31. Vvedenie v mikromehaniku / M. Onami, S. Ivasimidzu, K. Genka, K. Siodzava, K. Tanaka - M.: Metallurgia, 1987. - 280 c.
  32. Koiter W.T. Couple-stress in the theory of elasticity // Proc. Koenicl. Acad. Wet. - 1964. - Vol. B67. - P. 17.
  33. Kroener E. On the physical reality of torque stresses in continuum mechnics // Int. J. Eng. Sci. - 1963. - Vol. 1. - P. 261.
  34. Gauthier R.D., Jahsman W.E. A quest for micropolar elastic constants // Trans. ASME. - 1975. - Vol. E42. - No 2. - P. 369-374.
  35. Lakes R. Experimental methods for study of Cosserat elastic solids and other generalized elastic continua // Continuum models for materials with micro-structure. - N.-Y.: J. Wiley, 1995. - P. 1-22.
  36. Erofeev V.I. Volnovye processy v tverdyh telah s mikrostrukturoj. - M.: izd-vo Mosk. un-ta, 1999. - 328 s.
  37. Gauthier R.D., Jahsman W.E. A quest for micropolar elastic constants // Arch. Mech. - 1981. - Vol. 33. - No 5. - P. 717-737.
  38. Kules M.A., Matveenko V.P., Sardakov I.N. Postroenie i analiz tocnogo analiticeskogo resenia zadaci Kirsa v ramkah kontinuuma i psevdokontinuuma Kossera // PMTF. - 2001. - T. 42. - No 4. - S. 145-154.
  39. Kules M.A., Matveenko V.P., Sardakov I.N. Postroenie analiticeskih resenij nekotoryh dvumernyh zadac momentnoj teorii uprugosti // Izv. RAN. MTT. - 2002. - No 5. - S. 69-82.
  40. Kulesh M.A., Matveenko V.P., Shardakov I.N. Parametric analysis of analytical solutions to one-and twodimensional problems in couple-stress theory of elasticity // Z. Angew. Math. Mech. - 2003. - Vol. 83. - No 4. - P. 238-248.

Downloads

Published

2014-09-12

Issue

No. 2 (2014)

Section

Research: theory and experiment

How to Cite

Korepanov, V. . (2014). THE NUMERICAL ANALYSIS OF THE EXPERIMENTAL SCHEMES ON DETECTION OF COUPLE-STRESS EFFECTS UNDER STATIC AND DYNAMIC EXTERNAL FORCES. Perm Federal Research Centre Journal, 2, 13-22. https://journal.permsc.ru/index.php/pscj/article/view/PSCJ2014n2p2