Analytical and numerical solutions in the context of Cosserat continuum as the basis for experiments on detection of couple-stress effects in materials

Authors

  • Valery Valer'evich Korepanov Institute of Continuous Media Mechanics UB RAS
  • Mikhail Alexandrovich Kulesh Institute of Continuous Media Mechanics UB RAS
  • Valery Pavlovich Matveenko Institute of Continuous Media Mechanics UB RAS
  • Igor Nikolaevich Shardakov Institute of Continuous Media Mechanics UB RAS

DOI:

https://doi.org/10.7242/1999-6691/2009.2.4.33

Keywords:

Cosserat continuum, analytical and numerical solutions, experimental identification of parameters

Abstract

The analysis of analytical and numerical solutions to static problems obtained in the framework of the Cosserat continuum theory has been made for a special purpose to ascertain the effects due to couple-stress properties of materials. The appropriate macro-parameters have been identified and the measure of their response to couple-stress properties has been determined. A set of solutions, which are most informative from the view point of manifestation of couple-stress properties, has been found. These solutions have been used as a basis for development and realization of experiments on registration of couple-stress effects in the examined materials.

Downloads

Download data is not yet available.

References

Cosserat E. et F. Theorie des corps deformables. - Paris: Librairie Scientifique A. Hermann et Fils, 1909. - 226 p.
Ericksen J.L., Truesdell C. Exact theory of stress and strain in rods and shells // Arch. Rat. Mech. Anal. - 1958. - V. 1, N. 4. - P. 295-323. DOI
Tupin R.A. Teorii uprugosti, ucityvausie momentnye naprazenia. // Mehanika / Sb. per. - 1965. - No. 3. - S.113-140.
Toupin R.A. Elastic materials with couple-stress // Arch. Rat. Mech. Anal. - 1962. - V. 11, N. 5. - P. 385-399. DOI
Toupin R.A. Theories of elasticity with couple-stress // Arch. Rat. Mech. Anal. - 1964. - V. 17, N. 2. - P. 85-112. DOI
Mindlin R.D. Vlianie momentnyh naprazenij na koncentraciu naprazenij // Mehanika / Sb. per. - M.: Mir. - 1964. - No 4. - S. 115-128.
Mindlin R.D., Tirsten G.F. Effekty momentnyh naprazenij v linejnoj teorii uprugosti // Mehanika / Sb. per. - M.: Mir. - 1964. - No 4. - S. 80-114.
Mindlin R.D. Influence of couple-stress on stress concentrations // Experimental Mechanics. - 1963. - V. 3, N. 1. - P. 1-7. DOI
Mindlin R.D., Tierstin H.F. Effects of couple-stress in linear elasticity // Arch. Ration. Mech. and Analysis. - 1962. - V. 11, N. 5. - P. 415-488. DOI
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.
Aero E.L., Kuvsinskij E.V. Kontinual’naa teoria asimmetricnoj uprugosti. Ucet vnutrennego vrasenia // Fizika tverdogo tela. - 1964. - T. 6, vyp. 9. - C. 2689-2699.
Kuvsinskij E.V. Aero E.L. Kontinual’naa teoria asimmetricnoj uprugosti. Ucet vnutrennego vrasenia // Fizika tverdogo tela. - 1963. - T. 5, No 9. - S. 2591-2598.
Kojter V.T. Momentnye naprazenia v teorii uprugosti // Mehanika / Sb. per. - M.: Mir. - 1965. - No 3. - S. 89-112.
Koiter W.T. Couple-stress in the theory of elasticity // Proc. Kon. Nederland. Akad. Wetensch. - 1964. - V. 67. - P. 17-29, 30-44.
Pal’mov V.A. Osnovnye uravnenia teorii nesimmetricnoj uprugosti // PMM. - 1964. - T. 28, vyp. 3. - S. 401-408.
Green A.E., Rivlin R.S. Simple force and stress multipoles // Arch. Rat. Mech. Anal. - 1964. - V. 16, N 5. - P. 325-353.
Reissner E. On kinematics and statics in finite-strain force and moment stress elasticity // Stud. Appl. Math. - 1973. - V. 52, N. 2. - P. 97-101.
Novackij V. Teoria uprugosti. - M.: Mir, 1975. - 872 s.
Nowacki W. Couple-stresses in the theory of thermoelasticity // Bull. Acad. Polon. Sci. Ser. Sc. Techn. - 1966. - V. 14. - P. 505-512.
Erofeev V.I. Volnovye processy v tverdyh telah s mikrostrukturoj. - M.: Izd-vo Mosk. un-ta, 1999. - 328 s.
Eringen A.K. Teoria mikropolarnoj uprugosti // Razrusenie. - M.: Mir, 1975. - T. 2. - S. 646-751.
Zubov L.M. Nonlinear theory of dislocations and disclinations in elastic bodies. - Berlin: Heidelberg; N.Y.: Springer, 1997. - 205 p.
Nikitin E., Zubov L.M. Conservation lawsand conjugate solutions in the elasticity of simple materials and materials with couple stress // J. Elasticity. - 1998. - V. 51, N. 1. - P. 1-22. DOI
Erofeev V.I., Kazaev V.V., Semerikova N.P. Makromehaniceskoe modelirovanie uprugoj i vazko-uprugoj sred Kossera // Vycisl. meh. splos. sred. - Perm’, 2009. - T. 2, No 2. - S.40-47.
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.
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.
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.
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.
Nikolaevskij V.N. Geomehanika i fluidomehanika. - M.: Nedra, 1996. - 447 s.
Khurana A., Tomar S.K. Longitudinal wave response of a chiral slab interposed between micropolar solid half-spaces // Int. J. Solids Struct. - 2009. - N. 46. - P. 135-150. DOI
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. - N. 311. - P. 973-990. DOI
Tomar S.K., Khurana A. Elastic waves in an electro-microelastic solid // Int. J. Solids Struct. - 2008. - N. 45. - P. 276-302. DOI
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. - N. 5 (4). - P. 48-68.
Sadovskaa O.V. Cislennoe resenie prostranstvennyh dinamiceskih zadac momentnoj teorii uprugosti s granicnymi usloviami simmetrii // Z. vycisl. matematiki i matemat. fiziki. - 2009. - T. 49, No 2. - S. 313-322.
Korepanov V.V., Kules M.A., Matveenko V.P., Sardakov I.N. Analiticeskie i cislennye resenia staticeskih i dinamiceskih zadac nesimmetricnoj teorii uprugosti // Fizic. mezomehanika. - 2007. - T. 10, No 5. - S. 77-90.
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
Onami M., Ivasimidzu S., Genka K. Siodzava K., Tanaka K. Vvedenie v mikromehaniku. - M.: Metallurgia, 1987. - 280c.
Gauthier R.D., Jahsman W.E. A quest for micropolar elastic constants // Trans. ASME. - 1975. - V. E42, N. 2. - P. 369-374.
Ellis R.W., Smith C.W. A thin-plate analysis and experimental evaluation of couple-stress effects // Experimental Mechanics. - 1967. - V 7. - P. 372. DOI
Hoppman W.H., Shahwan F.O.F. Physical model of a 3-Constant isotropic elastic material // Transactions Trans. ASME. - 1965. - V. E32. - P. 837. DOI
Askar A. Molecular crystals and the polar theories of the continua (Experimental values of material coefficient for KNO3) // Int. J. Eng. Sci. - 1972. - V. 10. - P. 293. DOI
Perkins R.W., Thompson D. Experimental evidence of a couple-stress effect // AIAA Journal. American Institute of Aeronautics and Astronautics. - 1973. - V. 11. - P. 1053.
Cohen H. Dislocations in couple-stress elasticity // J. of Mathematics and Physics. - 1966. - V. 45. - P. 35.
Kroener E. On the physical reality of torque stresses in continuum mechnics // Int. J. Eng. Sci. - 1963. - V. 1. - P. 261. DOI
Koiter W.T. Couple-stress in the theory of elasticity // Proc. Koenicl. Acad. Wet. - 1964. - V. B67. - P. 17.
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.
Gauthier R.D., Jahsman W.E. A quest for micropolar elastic constants // Arch. Mech. - 1981. - V. 33, N. 5. - P. 717-737.
Kulesh M.A., Matveenko V.P., Shardakov I.N. Parametric analysis of analytical solutions to one- and two-dimensional problem in couple-stress theory of elasticity // Z. Angew. Math. Mech. (ZAMM) - 2003. - V. 83, N. 4. - P. 238-248. DOI
Kirsch G. Die theorie der eiastizi~t und die bed/irfnisse der festigkeislehre // Zantralblatt Berlin Deutscher Ingenieure, 1898. - P. 42.
Mushelisvili N.I. Nekotorye osnovnye zadaci matematiceskoj teorii uprugosti. - M.: Nauka, 1966. - 708 s.
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.
Kules M.A., Matveenko V.P., Sardakov I.N. Postroenie i analiz tocnogo analiticeskogo resenia zadaci Kirsa v ramkah kontinuuma i psevdokontinuuma Kossera // PMTF. - Novosibirsk, 2001. - T. 42, No 4. - S. 145-154.
Pal’mov V.A. Ploskaa zadaca teorii nesimmetricnoj uprugosti // PMM. - 1964. - T. 28, vyp. 6. - C. 1117-1120.

Downloads

Published

2009-07-01

Issue

Vol. 2 No. 4 (2009)

Section

Articles

License

Copyright (c) 2009 Computational Continuum Mechanics

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Korepanov, V. V., Kulesh, M. A., Matveenko, V. P., & Shardakov, I. N. (2009). Analytical and numerical solutions in the context of Cosserat continuum as the basis for experiments on detection of couple-stress effects in materials. Computational Continuum Mechanics, 2(4), 76-91. https://doi.org/10.7242/1999-6691/2009.2.4.33