Characteristic constitutive numbers in semi isotropic coupled thermoelasticity

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

In continuum mechanics (especially in hydroaeromechanics), methods of modeling flow (deformation) by characteristic numbers are widely used. The present study is devoted to the search for characteristic combinations of constitutive thermoelastic modules, geometric and thermomechanical parameters of the boundary value problem. Modeling the micropolar solids deformation by characteristic numbers is characterized by a sufficiently large number (13) of constitutive modules. The constitutive equations, the dynamic equations and the heat conduction equation for a semi-isotropic micropolar thermoelastic continuum are derived in a linear approximation. A dimensional analysis of the governing system of differential equations is carried out. A physically consistent series (9 primary and several arbitrary) of dimensionless characteristic combinations of constitutive constants is proposed. The characteristic numbers for harmonic waves propagating along the axis of a stress free thermally insulated long cylindrical semi-isotropic thermoelastic waveguide are obtained and discussed.

About the authors

E. V. Murashkin

Ishlinsky Institute for Problems in Mechanics RAS

Author for correspondence.
Email: murashkin@ipmnet.ru
Russian Federation, Moscow

Y. N. Radayev

Ishlinsky Institute for Problems in Mechanics RAS

Email: radayev@ipmnet.ru
Russian Federation, Moscow

References

  1. Lakes R. Composites and Metamaterials. Singapore: World Scientific, 2020.
  2. Radayev Y.N. The Lagrange multipliers method in covariant formulations of micropolar continuum mechanics theories // Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki. 2018. V. 22. № 3. P. 504–517. https://doi.org/10.14498/vsgtu1635
  3. Murashkin E.V., Radayev Y.N. On the theory of linear micropolar hemitropic media // Vestn. Chuvash. Gos. Ped. Univ. Im. I.Ya. Yakovleva. Ser.: Mekh. Pred. Sost. 2020. V. 4. № 46. P. 16–24. https://doi.org/10.37972/chgpu.2020.89.81.031
  4. Murashkin E.V., Radayev Y.N. Coupled thermoelasticity of hemitropic media. pseudotensor formulation // Mech. Solids. 2023. V. 58. № 3. P. 802–813. http://doi.org/10.3103/s0025654423700127
  5. Murashkin E.V., Radayev Y.N. On the polyvariance of the base equations of coupled micropolar thermoelasticity // Vestn. Chuvash. Gos. Ped. Univ. Im. I.Ya. Yakovleva. Ser.: Mekh. Pred. Sost. 2023. V. 3. № 57. P. 112–128. https://doi.org/10.37972/chgpu.2023.57.3.010
  6. Murashkin E.V., Radayev Y.N. Multiweights thermomechanics of hemitropic micropolar solids // Vestn. Chuvash. Gos. Ped. Univ. Im. I.Ya. Yakovleva. Ser.: Mekh. Pred. Sost. 2023. V. 4. № 58. P. 86–120. https://doi.org/10.37972/chgpu.2023.58.4.010
  7. Murashkin E.V., Radayev Y.N. Pseudotensor formulation of the mechanics of hemitropic micropolar media // Probl. Prochn. Plastichn. 2020. V. 82. № 4. P. 399–412. https://doi.org/10.32326/1814-9146-2020-82-4-399-412
  8. Murashkin E.V., Radayev Y.N. On a micropolar theory of growing solids // Vestn. Samarsk. Gos. Tekh. Univ. Ser. Fiz.-Mat. Nauki. 2020. V. 24. № 3. P. 424–444. https://doi.org/10.14498/vsgtu1792
  9. Cosserat E., Cosserat F. Théorie des Corps Déformables. Paris: Herman et Fils, 1909. vi+226 p.
  10. Nowacki W. Theory of Micropolar Elasticity. Berlin: Springer, 1972. 285 p
  11. Nowacki W. Theory of Asymmetric Elasticity. Oxford: Pergamon Press, 1986. 383 p.
  12. Kovalev V.A., Murashkin E.V., Radayev Y.N. On the Neuber theory of micropolarelasticity. A pseudotensor formulation // Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki. 2020. V. 24. № 4. P. 752–761. https://doi.org/10.14498/vsgtu1799
  13. Gurevich G.B. Foundations of the Theory of Algebraic Invariants. M., L.: GITTL, 1948; Groningen: Noordhoff, 1964.
  14. McConnell A.J. Application of Tensor Analysis. NY: Dover Publ. Inc., 1957.
  15. Sokolnikoff I.S. Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua. John Wiley & Sons Inc, 1964; M.: Nauka, 1971.
  16. Schouten J.A. Tensor Analysis for Physicist. Oxford: Clarendon Press, 1965.
  17. Synge J.L., Schild A. Tensor Calculus. Courier Corporation, 1978.
  18. Kovalev V.A., Radayev Y.N. Elements of the Classical Field Theory: Variational Symmetries and Geometric Invariants. M.: Fizmatlit, 2009 [in Russian].
  19. Kovalev V.A., Radayev Y.N. Wave Problems of Field Theory and Thermomechanics. Saratov: Saratov Univ., 2010 [in Russian].
  20. Birkhoff G. Hydrodynamics: A Study in Logic, Fact, and Similitude. Dover Publications, 1955.
  21. Sedov L.I. Similarity and Dimensional Methods in Mechanics. M.: Nauka, 1977; Boca Raton: CRC Press, 1993. https://doi.org/10.1201/9780203739730
  22. Kutateladze S.S. Analysis of Similarity and Physical Models. Novosibirsk: Nauka, 1986 [in Russian].
  23. Barenblatt G.I. Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics. Cambridge: Cambridge Univ. Press, 1996. https://doi.org/10.1017/CBO9781107050242
  24. Zohuri B. Similitude theory and applications. In: Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists. Cham: Springer, 2015. P. 93–193. https://doi.org/10.1007/978-3-319-13476-5_2
  25. Loitsyansky L.G. Mechanics of Liquids and Gases. M.: Nauka, 1950; NY: Begell House, 1995.
  26. Murashkin E.V., Radayev Y.N. Multiweights thermomechanics of hemitropic micropolar solids // Vestn. Chuvash. Gos. Ped. Univ. Im. I.Ya. Yakovleva. Ser.: Mekh. Pred. Sost. 2023. V. 4. № 58. P. 86–120. https://doi.org/10.37972/chgpu.2023.58.4.010
  27. Murashkin E.V., Radayev Y.N. Coupled thermoelasticity of hemitropic media. pseudotensor formulation // Mech. Solids. 2023. V. 58. № 9. P. 802–813. http://doi.org/10.3103/s0025654423700127
  28. Murashkin E.V., Radayev Y.N. Heat conduction of micropolar solids sensitive to mirror reflections of three-dimensional space // Uch. Zap. Kazan. Univ. Ser. Fiz.-Mat. Nauki. 2023. V. 165. № 4. P. 389–403. https://doi.org/10.26907/2541-7746.2023.4.389-403
  29. Jeffreys H. Cartesian Tensors. Cambridge Univ. Press, 1931.
  30. Radayev Y.N. Tensors with constant components in the constitutive equations of hemitropic micropolar solids // Mech. Solids. 2023. V. 58. № 5. P. 1517–1527. https://doi.org/10.3103/S0025654423700206
  31. Murashkin E.V., Radayev Y.N. Covariantly constant tensors in Euclidean spaces. Elements of the theory // Vestn. Chuvash. Gos. Ped. Univ. Im. I.Ya. Yakovleva. Ser.: Mekh. Pred. Sost. 2022. V. 2. № 52. P. 106–117. https://doi.org/10.37972/chgpu.2022.52.2.012
  32. Murashkin E.V., Radayev Y.N. Covariantly constant tensors in Euclidean spaces. Applications to continuum mechanics // Vestn. Chuvash. Gos. Ped. Univ. Im. I.Ya. Yakovleva. Ser.: Mekh. Pred. Sost. 2022. V. 2. № 52. P. 118–127. https://doi.org/10.37972/chgpu.2022.52.2.013
  33. Murashkin E.V., Radayev Y.N. Reducing natural forms of hemitropic energy potentials to conventional ones // Vestn. Chuvash. Gos. Ped. Univ. Im. I.Ya. Yakovleva. Ser.: Mekh. Pred. Sost. 2022. V. 4. № 54. P. 108–115. https://doi.org/10.37972/chgpu.2022.54.4.009
  34. Murashkin E.V., Radayev Y.N. On two base natural forms of asymmetric force and couple stress tensors of potential in mechanics of hemitropic solids // Vestn. Chuvash. Gos. Ped. Univ. Im. I.Ya. Yakovleva. Ser.: Mekh. Pred. Sost. 2022. V. 3. № 53. P. 86–100. https://doi.org/10.37972/chgpu.2022.53.3.010
  35. Murashkin E.V. On the relationship of micropolar constitutive parameters of thermodynamic state potentials // Vestn. Chuvash. Gos. Ped. Univ. Im. I.Ya. Yakovleva. Ser.: Mekh. Pred. Sost. 2023. V. 1. № 55. P. 110–121. https://doi.org/10.37972/chgpu.2023.55.1.012
  36. Murashkin E.V., Radayev Y.N. On a ordering of area tensor elements orientations in a micropolar continuum immersed in an external plane space // Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki. 2021. V. 25. № 4. P. 776–786. https://doi.org/10.14498/vsgtu1883
  37. Murashkin E.V., Radayev Y.N. On theory of oriented tensor elements of area for a micropolar continuum immersed in an external plane space // Mech. Solids. 2022. V. 57. № 2. P. 205–213. http://doi.org/10.3103/s0025654422020108
  38. Murashkin E.V., Radayev Y.N. The schouten force stresses in continuum mechanics formulations // Mech. Solids. 2023. V. 58. № 1. P. 153–160. http://doi.org/10.3103/s0025654422700029

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2024 Russian Academy of Sciences